The correct option is B ( x 4 ) ( 4+x ) ( x+9 ) ( 9 x ) 25x^2 ( x^2 36 )^2 = #160; ( 5x )^2 ( x^2 36 )^2 = #160; ( 5x+x^2 36 ) ...

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Algebra of Derivatives

25x2- x2-36 2...

Question

$25 x^{2} - {(x^{2} - 36)}^{2}$ =_______

(x - 4) (x + 4) (x + 9) (x - 9)

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(x - 4) (4 + x) (x + 9) (9 - x)

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(x + 4) (x + 4) (x - 9) (x - 9)

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(x - 4) (4 - x) (x + 9) (9 + x)

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Solution

The correct option is B $(x - 4) (4 + x) (x + 9) (9 - x)$
$25 x^{2} - {(x^{2} - 36)}^{2}$
= ${(5 x)}^{2} - {(x^{2} - 36)}^{2}$
= $(5 x + x^{2} - 36) (5 x - x^{2} + 36)$
= $(x^{2} + 5 x - 36) {- (x^{2} - 5 x - 36)}$
= $(x^{2} + 9 x - 4 x - 36) {- (x^{2} - 9 x + 4 x - 36)}$
= ${x (x + 9) - 4 (x + 9)} {- (x (x - 9) + 4 (x - 9))}$
= $(x + 9) (x - 4) - (x - 9) (x + 4)$
= $(x + 9) (x - 4) (9 - x) (4 + x)$

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If

x^{2} - 9 x + 20 = (x - 4) (x - a)

then

a =

4 x^{7} + 3 x^{6} + 2 x^{5} + 9 x^{4} + 4 x^{3} + x^{2} + 9 x + 9 = 0

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