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# Simplify : X 2 − 5 X − 24 ( X + 3 ) ( X + 8 ) × X 2 − 64 ( X − 8 ) 2 - SSC (English Medium) Class 8 - Mathematics

#### Question

Simplify :

$\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}$

#### Solution

It is known that,

$a^2 - b^2 = \left( a + b \right)\left( a - b \right) ; a^3 - b^3 = \left( a - b \right)\left( a^2 + ab + b^2 \right)$

$\ \frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}$

$= \frac{x^2 - 8x + 3x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x \right)^2 - \left( 8 \right)^2}{\left( x - 8 \right)^2}$

$= \frac{x\left( x - 8 \right) + 3\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}$

$= \frac{\left( x + 3 \right)\left( x - 8 \right)}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{\left( x + 8 \right)\left( x - 8 \right)}{\left( x - 8 \right)\left( x - 8 \right)}$

$= 1$

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#### APPEARS IN

Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.4 | Q: 4 | Page no. 33
Solution Simplify : X 2 − 5 X − 24 ( X + 3 ) ( X + 8 ) × X 2 − 64 ( X − 8 ) 2 Concept: Factors of A3 - B3.
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