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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