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

EXERCISE 12 C

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

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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)

$=\frac{264}{440}x^5y^3$

$=\frac{3}{5}x^5y^3$

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

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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

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

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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

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

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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