Simplify- x2-1x2-3x-2x3-6x2x2-x

Given, x^2 1x^2+3x×2x^3+6x^2x^2+x =(x 1)(x+1)x(x+3)×2x^2(x+3)x(x+1) =(x 1)(x+1)× 2x^2(x+3)x(x+3)× x(x+1) =2(x 1)=2x 2 ...

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Byju's Answer

Standard VIII

Mathematics

Properties of Square Numbers

Simplify: x2...

Question

Simplify: $\frac{x^{2} - 1}{x^{2} + 3 x} \times \frac{2 x^{3} + 6 x^{2}}{x^{2} + x}$

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Solution

given, $\frac{x^{2} - 1}{x^{2} + 3 x} \times \frac{2 x^{3} + 6 x^{2}}{x^{2} + x}$

$= \frac{(x - 1) (x + 1)}{x (x + 3)} \times \frac{2 x^{2} (x + 3)}{x (x + 1)}$

$= \frac{(x - 1) (x + 1) \times 2 x^{2} (x + 3)}{x (x + 3) \times x (x + 1)}$

$= 2 (x - 1) = 2 x - 2$

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Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

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(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

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Simplify:x2−1x2+3x×2x3+6x2x2+x

given, x2−1x2+3x×2x3+6x2x2+x=(x−1)(x+1)x(x+3)×2x2(x+3)x(x+1)=(x−1)(x+1)×2x2(x+3)x(x+3)×x(x+1)=2(x−1)=2x−2

Simplify: $\frac{x^{2} - 1}{x^{2} + 3 x} \times \frac{2 x^{3} + 6 x^{2}}{x^{2} + x}$

given, $\frac{x^{2} - 1}{x^{2} + 3 x} \times \frac{2 x^{3} + 6 x^{2}}{x^{2} + x}$

$= \frac{(x - 1) (x + 1)}{x (x + 3)} \times \frac{2 x^{2} (x + 3)}{x (x + 1)}$

$= \frac{(x - 1) (x + 1) \times 2 x^{2} (x + 3)}{x (x + 3) \times x (x + 1)}$

$= 2 (x - 1) = 2 x - 2$