Showing posts with label Fundamental concept and operations. Show all posts
Showing posts with label Fundamental concept and operations. Show all posts

S.chand composite class 8 mathematics solution chapter 12 Fundamental concept and Operations exercise 12 D

EXERCISE 12 D

Q1 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper


QUESTION 1

Divide

(i) 28a3b2c by 7ab

Sol :

$=\frac{28a^3b^2c}{7ab}$

=4a2bc


(ii) 48a4b5c6 by - 16a2c2

Sol :

$=\frac{48a^4b^5c^6}{- 16a^2c^2}$

=-3a2b5c4


(iii) $-\dfrac{4}{5}a^2b^2c^4 \text{ by } -\dfrac{6}{15}abc^2$

Sol :

$=\dfrac{-\frac{4}{5}a^2b^2c^4}{-\frac{6}{15}abc^2}$

$=-\frac{4}{5}\times -\frac{15}{6}=\frac{60}{30}$

=2abc2


Q2 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 2

Divide :

(i) 16pr2-8pr3-4p2r2 by -4pr2

Sol :

$=\frac{16pr^2-8pr^3-4p^2r^5}{-4pr^2}$

$=\frac{16pr^2}{-4pr^2}+\frac{-8pr^3}{-4pr^2}+\frac{-4p^2r^5}{-4pr^2}$

=-4+2r+pr3


(ii) 6x7-8x6+4x5-10x4+6x3 by -2x3

Sol :

$=\frac{6x^7-8x^6+4x^5-10x^4+6x^3}{-2x^3}$

$=\frac{6x^7}{-2x^3}+\frac{-8x^6}{-2x^3}+\frac{+4x^5}{-2x^3}+\frac{-10x^4}{-2x^3}+\frac{+6x^3}{-2x^3}$

=-3x4+4x3-2x2+5x-3


(iii) 7x4y2-14x3y3+35x2y4-56x7y5+21y6 by 7x2y2

Sol :

$=\frac{7x^4y^2}{7x^2y^2}-\frac{14x^3y^3}{7x^2y^2}+\frac{35x^2y^4}{7x^2y^2}-\frac{56x^7y^5}{7x^2y^2}+\frac{21y^6}{7x^2y^2}$

=x2-2xy+5y2-8x5y3+$\frac{3y^4}{x^2}$


(iv) $\dfrac{3}{5}abc-\dfrac{2}{5}a^2bc^2+\dfrac{1}{7}ab^2 \text{ by } \dfrac{1}{3}abc$

Sol :

=$\dfrac{\frac{3}{5}abc}{\frac{1}{3}abc}-\dfrac{\frac{2}{5}a^2bc^2}{\frac{1}{3}abc}+\dfrac{\frac{1}{7}ab^2}{\frac{1}{3}abc}$

$=\left(\frac{3}{4}\times \frac{3}{1}\right)-\left(\frac{2}{5}\times \frac{3}{1}\right)ac+\left(\frac{1}{7}\times \frac{3}{1}\right)\frac{b}{c}$

$=\frac{9}{4}-\frac{6}{5}ac+\frac{3b}{7c}$


Q3 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 3

Divide :

(i) (x2+8x+15) by (x+3)

Sol :

$\begin{array}{l}x+3\overline{)+x^2+8x+15(}x+5\\\phantom{x+3}+x^2+3x\\\phantom{x+3}-\phantom{x^2}-\phantom{3x}\\ \phantom{x+3)}\overline{\phantom{x^2} +5x+15}\\\phantom{x+3)x^2}+5x+15\\\phantom{x+3)x^2}-\phantom{5x}-\phantom{15 }\\\phantom{x+3)x^2} \overline{\phantom{+5x+1}0}\end{array}$


(ii) (2x2+7x+6) by (x+2)

Sol :

$\begin{array}{l}x+2\overline{)+2x^2+7x+6(}2x+3\\\phantom{x+2}+2x^2+4x\\\phantom{x+2}-\phantom{2x^2}-\phantom{4x} \\ \phantom{x+2)}\overline{\phantom{2x^2}+3x+6}\\\phantom{x+2)2x^2}+3x+ 6\\\phantom{x+2)2x^2}-\phantom{3x}-\phantom{6} \\\phantom{x+2)2x^2} \overline{\phantom{+3x+6}0}\end{array}$

(iii) (-2x2-3x+2) by (x+2)

Sol :

$\begin{array}{l}x+2\overline{)-2x^2-3x+2(}-2x+1\\ \phantom{x+2}-2x^2-4x\\\phantom{x+2}+\phantom{2x^2}+\phantom{4x}\\\phantom{x+2}\overline{\phantom{+2x^2}+1x+2}\\\phantom{x+2+2x}+1x+2\\\phantom{x+2+2x}-\phantom{1x}-\phantom{2}\\\phantom{x+2+2x^2}\overline{\phantom{+1x+2}0}\end{array}$


(iv) (12x2+7xy-10y2) by (3x-2y)

Sol :

$\begin{array}{l}3x-2y\overline{)+12x^2+7xy-10y^2(}4x+5y\\\phantom{3x-2y}+12x^2-8xy\\\phantom{3x-2y}-\phantom{12x^2}+\phantom{8xy}\\ \phantom{3x-2y}\overline{\phantom{-12x^2}+15xy-10y^2}\\ \phantom{3x-2y-12x}+15xy-10y^2\\ \phantom{3x-2y-12x}-\phantom{15xy}+\phantom{10y^2}\\\phantom{3x+2y-12x^2}\overline{\phantom{+15xy+10y^2}0} \end{array}$


(v) (6+x-4x2+x3) by (x-3)

Sol :

$\begin{array}{l}x-3\overline{)+x^3-4x^2+x+6(}x^2-x-2\\\phantom{x-3}+x^3-3x^2\\\phantom{x-3}-\phantom{x^2}+\phantom{3x^2}\\\phantom{x-3)}\overline{\phantom{-x^3}-x^2+x}\\\phantom{x-3-x^3}-x^2+3x\\\phantom{x-3-x^3}+\phantom{x^2}-\phantom{3x}\\\phantom{x-3)-x^3}\overline{\phantom{+x^2}-2x+6}\\\phantom{x-3-x^3+x^2}-2x+6\\\phantom{x-3-x^3+x^2}\overline{\phantom{+2x+6}0}\end{array}$


(vi) (x3-125y3-15x2y+75xy2) by (x-5y)

Sol :

$\begin{array}{l}x-5y\overline{)+x^3-15x^2y+75xy^2-125y^3(}x^2-10xy+25y^2\\\phantom{x-5y}+x^3-5x^2y\\\phantom{x-5y}-\phantom{x^3}+\phantom{5x^2y}\\\phantom{x-5y)}\overline{\phantom{-x^3}-10x^2y+75xy^2}\\\phantom{x-5y)}\phantom{-x^3}-10x^2y+50xy^2\\\phantom{x-5y)}\phantom{-x^3}+\phantom{10x^2y}-\phantom{75xy^2}\\\phantom{x-5y)-x^2}\overline{\phantom{+10x^2y}+25xy^2-125y^3}\\\phantom{x-5y)-x^2}\phantom{+10x^2y}+25xy^2-125y^3\\\phantom{x-5y)-x^2}\phantom{+10x^2y}-\phantom{25xy^2}+\phantom{125y^3}\\\phantom{x-5y)-x^3+10x^2y}\overline{\phantom{-25xy^2}0\phantom{+125y^3}}\end{array}$


Q4 | Ex-12D | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 4

Divide :

(i) x3-125 by (x-5)

Sol :








(ii) 64a3+27b3 by (4a+3b)

Sol :









(iii) (a4-16) by (a+2)

Sol :









(iv) x5-y5 by (x-y)

Sol :









 

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S.chand class 8 composite mathematics solution chapter 12 Fundamental concept and Operations exercise 12 C

EXERCISE 12 C

Q1 | Ex-12C | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper


QUESTION 1

Multiply :

(i) 12xy by -8x2

Sol :

=12xy×(-8x2)

=(12×8)×(x1×x2)×y

=-96x3y


(ii) -16a2b2 by -5ab2

=-16a2b2×(-5ab2)

=(-16×-5)×(a2×a1)×(b2×b2)

=80a3b4


(iii) $\left(\dfrac{3}{5}a^2b^2\right) \text{ by } \left(\dfrac{10}{27}ab^4\right)$

Sol :

=$\left(-\frac{3}{5}\times \frac{10}{27}\right)$×(a2×a1)×(b2×b4)

$=-\frac{30}{135}a^3b^6$

$=-\frac{2}{9}a^3b^6$


(iv) $\left(\frac{4}{3}x^2y^5\right) \text{ by } \left(\frac{6}{7}x^2y^3\right)$

Sol :

=$\left(\frac{4}{3}\times \frac{6}{7}\right)$×(x2×x2)×(y5×y3)

=$\frac{24}{21}x^4y^8=\frac{8}{7}x^4y^8$


(v) $\left(-\frac{11}{8}xy^3\right) \text{ by }\left(-\frac{24}{55}x^4\right)$
Sol :
=$\left(-\frac{11}{8}xy^3\right) \times \left(-\frac{24}{55}x^4\right)$
=$-\left(\frac{11}{8}\times \frac{24}{55}\right)$×(x1×x4)×(y3)
$=\frac{264}{440}x^5y^3$
$=\frac{3}{5}x^5y^3$


Q2 | Ex-12C | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 2

Multiply :

(i) (6x-5) by -3x

=(6x-5)×-3x

=(6x×3x)-5×-3x

=-18x2+15x


(ii) (12x2-4x+5) by 8x3

Sol :

=(12x2-4x+5)×8x3

=(12x2×8x3)-(4x×8x3)+(5×8x3)

=96x5-4x4+40x3


(iii) (3a3x3-4ay2+7a2y) by -4x2ya2

Sol :
=(3a3x3-4ay2+7a2y)×(-4x2ya2)
=(3a3x3×-4x2ya2)+(-4ay2×-4x2ya2)+(7a2y×-4x2ya2)
=-12a5yx5+16a3y3x2-28x2y2a4


Q3 | Ex-12C | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 3

Find the product :

(i) (x+6)(x+11)

Sol :

=x(x+11)+6(x+11)

=x2+11x+6x+66

=x2+17x+66


(ii) (2a+5)(3a-6)

Sol :

=2a(3a-6)+5(3a-6)

=6a2-12a+15a-30

=6a2+3a-30


(iii) (5x+2b)(5x-2b)

Sol :

=5x(5x-2b)+2b(5x-2b)

=25x2-10xb+10xb-4b2

=25x2-4b2


(iv) (6x2-11x+7)(3x-4)

Sol :

=3x(6x2-11x+7)-4(6x2-11x+7)
=3x(6x2-11x+7)-4(6x2-11x+7)
=18x3-33x2+21x-24x2+44x-28
=18x3-33x2-24x2+21x+44x-28
=18x3-57x2+65x-28


(v) (2x2-3x-1)(x-5)

Sol :

=x(2x2-3x-1)-5(2x2-3x-1)

=2x3-3x2-x-10x2+15x+5

=2x3-3x2-10x2-x+15x+5

=2x3-13x2+14x+5


(vi) (a4-a2b2+b4)(a2+b2)

Sol :

=a2(a4-a2b2+b4)+b2(a4-a2b2+b4)

=a6-a4b2+a2b4+a4b2-a2b4+b6

=a6+b6


Q4 | Ex-12C | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 4

Multiply :

(i) (a-b+c) by (a-b-c)

Sol :

=(a-b+c)(a-b-c)

=a(a-b-c)-b(a-b-c)+c(a-b-c)

=a2-ab-ac-ab+b2+bc+ac-bc-c2

=a2+b2-c2-ab-ab-ac+ac+bc-bc

=a2+b2-c2-2ab


(ii) (x3-4x2+5x-2) by (x2+2x-1)

Sol :

=x2(x3-4x2+5x-2)+2x(x3-4x2+5x-2)-1(x3-4x2+5x-2)

=x5-4x4+5x3-2x2+2x4-8x3+10x2-4x-x3+4x2-5x+2

=x5-4x4+2x4+5x3-8x3-x3-2x2+10x2+4x2-4x-5x+2

=x5-2x4-4x3+12x2-9x+2


(iii) (2x2-5x+3) by (5x2-6x-4)

Sol :

=5x2(2x2-5x+3)-6x(2x2-5x+3)-4(2x2-5x+3)

=10x4-25x3+15x2-12x3+30x2-18x-8x2+20x-12

=10x4-25x3-12x3+15x2+30x2-8x2-18x+20x-12

=10x4-37x3+37x2+2x-12


(iv) (3x4-x2+6x-7) by (x2-3x+4)

Sol :

=x2(3x4-x2+6x-7)-3x(3x4-x2+6x-7)+4(3x4-x2+6x-7)

=3x6-x4+6x3-7x2-9x5+3x3-18x2+21x+12x4-4x2+24x-28

=3x6-9x5+11x4+9x3-29x2+45x-28

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S.chand books class 8 maths solution chapter 12 Fundamental concept and Operations exercise 12 B

 EXERCISE 12 B

Q1 | Ex-12B | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper



QUESTION 1

Add the following expressions

(i) 2ab+3b and 5ab+7b

Sol:  

=2ab+3b+5ab+7b

=2ab+3b+5ab+7b

=7ab+10b


(ii) 2x2+3xy and 6xy-4x2

Sol :

=2x2+3xy+6xy-4x2

=2x2-4x2+3xy+6xy

=-2x2+9xy


(iii) 5z2-11z+7 and 10z2-18+7z

Sol :

=5z2-11z+7+10z2-18+7z

=5z2+10z2-11z+7z+7-18

=15z2-4z-11


(iv) y3-3y2+7y-17 and 2y2-5y-8y3+20

Sol :

=y3-3y2+7y-17+2y2-5y-8y3+20

=y3-8y3-3y2+2y2+7y-5y-17+20

=7y3-y2+2y+3


(v) 4x2-7xy+8z and x2-2xy+9z and -3x2+8xy

Sol :

=4x2-7xy+8z+x2-2xy+9z-3x2+8xy

=4x2+x2-3x2-7xy-2xy+8xy+8z+9z

=2x2-xy+17z


Q2 | Ex-12B | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper


QUESTION 2

Subtracted as indicated :

(i) (4a-5b-c)-(3a+2b-7c)

Sol :

=(4a-5b-c)-(3a+2b-7c)

=4a-5b-c-3a-2b+7c

=4a-3a-5b-2b-c+7c

=a-7b+6c


(ii) 4x2-5x+3 from 4x2-3x+2

Sol :

=(4x2-3x+2)-(4x2-5x+3)

=4x2-3x+2-4x2+5x-3

=4x2-4x2-3x+5x+2-3

=2x-1


(iii) 4xy-8+y2 from 5x2+6xy-6

Sol :

=(5x2+6xy-8)-(4xy-6+y2)

=5x2+6xy-8-4xy+6-y2

=5x2-y2+6xy-4xy-8+6

=5x2-y2+2xy-2


(iv) (-4x2-x+9)-(3x2-x)

Sol :

=-4x2-x+9-3x2+x

=-4x2-3x2-x+x+9

=-7x2+9

 

Q3 | Ex-12B | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 3

From the sum of x+3y and -3x-y subtract x-y

Sol :

=[x+3y-3x-y]-(x-y)

=[x-3x+3y-y]-(x-y)

=-2x+2y-x+y

=-2x-x+2y+y

=-3x+3y

 

Q4 | Ex-12B | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 4

Subtract a2-b2-c2 from the sum of 2a2+3b2-c2 and 4a2-3b2+5c2

Sol :

=(2a2+3b2-c2+4a2-3b2+5c2)-(a2-b2-c2)

=(2a2+4a2+3b2-3b2-c2+5c2)-a2+b2+c2

=(6a2+4c2)-a2+b2+c2

=6a2+4c2-a2+b2+c2

=6a2-a2+4c2+c2+b2

=5a2+5c2+b2

 

Q5 | Ex-12B | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | myhelper

QUESTION 5

Subtract the sum of (4x3+2x2-5) and (15x-x3-x2) from the sum of (9+6x-2x2) and (4x-1-5x3+x2)

Sol :

=[(9+6x-2x2) and (4x-1-5x3+x2)-(4x3+2x2-5) and (15x-x3-x2)]

=[(9+6x-2x2+4x-1-5x3+x2)-(4x3+2x2-5+15x-x3-x2)]

=[(-5x3-2x2+x2+4x+6x-1+9)-(4x3-x3+2x2-x2+15x-5)]

=[(-5x3-x2+10x+8)-(3x3+x2+15x-5)]

=-5x3-x2+10x+8-3x3-x2-15x+5

=-5x3-3x3-x2-x2+10x-15x+8+5

=-8x3-2x2-5x+13

 

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S.chand composite mathematics solution class 8 chapter 12 Fundamental concept and operations

EXERCISE 12 A

Q1 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper


QUESTION 1

Which of the following expressions are not polynomials ?

(i) $\dfrac{1}{2}x^2-6x-\dfrac{1}{7}+x^3$

Sol :

Yes , its a polynomial

 

(ii) $10p^2 + \dfrac{7}{p}-2$

Sol :

$10p^2+7p^{-1}-2$  [∴ $\dfrac{1}{P}=P^{-1}$]

No , its not a polynomial since it contains negative exponent(power)

 

(iii) $5z^3-\sqrt{7}z^2 +11$

Sol :

Yes , it is a polynomial

 

(iv) $\dfrac{5x-8x^2}{1+x}$

Sol :

$\begin{array}{l}x+1\overline{)-8x^2+5x~(}-8x+13-\tfrac{13}{x}\\\phantom{x+1}-8x^2-8x\\\phantom{x+1}\underline{+\phantom{8x^2}+\phantom{8x}}\\\phantom{x+1}\phantom{-8x^2}+13x\\\phantom{x+1}\phantom{-8x^2}+13x+13\\\phantom{x+1}\phantom{-8x^2}\underline{-\phantom{13x}-\phantom{13}}\\\phantom{x+1}\phantom{-8x^2+13x}-13\\\phantom{x+1}\phantom{-8x^2+13x}-13-\frac{13}{x}\end{array}$

No 

 

(v) $\sqrt{3}x^{\tfrac{1}{2}}+5x^2-9x^2+7$

Sol :

No , because power is in fraction .


(vi) $x^2+\dfrac{1}{x^2}$

Sol :

No, its not a polynomial since it contains negative exponent(power)


(vii) 2x4-7x2+5x-2

Sol :

Yes, It'a a polynomial


(viii) 45

Sol :

Yes, It'a a polynomial


(ix) $\dfrac{x}{2}+5$

Sol :

Yes, It'a a polynomial

 

(x) $7x^{-2}+x^{-1}+8$

Sol :

No

Q2 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

QUESTION 2

Write monomial , binomial , trinomial or polynomial to classify each polynomial and also state their degree :

[Term : A product of a number and one or more variables with exponents.

Degree : Degree of a polynomial is defined as the highest power of the variable of its individual terms]

(i) 5x

Sol :

Here, expression contains only one term '5x'. So, it is a monomial

Degree : 1 


(ii) 17x3y2z

Sol :

Monomial because it contains one term

Degree : 6


(iii) -11-7x

Sol :

Binomial because it contains two terms

Degree : 1

 

(iv) x2 + 3x + 7

Sol :

Trinomial because it contains three terms

Degree : 2


(v) $-z+\sqrt{3}z^3$

Sol :

Binomial because it contains two terms

Degree : 3


(vi) m-8m2+m4-2m2

Sol :

Polynomial because it contains more than 3 terms

Degree : 4


(vii) y4-3y2+19

Sol :

Trinomial because it contains three terms

Degree : 4

 

(viii) $\dfrac{1}{2}p^4-3p+5-p^6+11p^3$

Sol :

Polynomial because it contains more than 3 terms

Degree : 6


Q3 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

QUESTION 3

Arrange the polynomial 4x2y2-7xy3+2x4-3y4+x3y in decreasing degree in x

Sol :

 2x4+x3y+4x2y2-7xy3-3y4


Q4 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

QUESTION 4

Give the degree of each of the following polynomials :

(i) 5x3 + 6x2 - 3x + 20

Sol :

Degree : 3


(ii) -2x + 9

Sol :

Degree : 1


(iii) x2y3 + 5x2 - 9xy

Sol :

Degree : 5


(iv) -23

Sol :

Degree : 0


Q5 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

QUESTION 5

Write down the numerical as well as literal coefficients of the following monomials

(i) 2πr

Sol :

Numerical coefficient : 2π

Literal coefficient : r


(ii) 6x2y2

Sol :

Numerical coefficient : 6

Literal coefficient : x2y2


(iii) -5ab2

Sol :

Numerical coefficient : -5

Literal coefficient : ab2


(iv) $\dfrac{4}{3}abc$

Sol :

Numerical coefficient : $\frac{4}{3}$

Literal coefficient : abc


 

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