Question

$27 - 125a {}^{3} - 135a + 225a {}^{2}$ Please factorise​

Answer 1

for solving this question you should use the polynomial identity (a - b)³ = a³ - b³ -3ab (a-b).

Given, a = 3 ( because 3 is cube root of 27)

b = -5a (because 5 is cube root of 125).

(3)³ - (-5a)³ - 3 (3)(-5a) { 3 + (-5a) }

27 - 125a³ - 45a ( 3 + (-5a) ) = ( multiply 45a with 3 and -5a and get the answer)

27 -125a³ -135a -225 a².

Hence this answer is verified.

Answer 2

$\sf{\red{\boxed{\bold{Solution}}}}$

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$\sf:\implies\:{\bold{ 27 + 125a^3 + 135a + 225a^2}}$

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$\sf:\implies\:{\bold{ (3)^3 + (5a)^3 + 135a + 225a^2}}$

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$\sf:\implies\:{\bold{ (3)^3 + (5a)^3 + 45a( 3 + 5a ) }}$

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$\sf:\implies\:{\bold{ (3)^3 + (5a)^3 + 3\times 3\times 5a( 3 + 5a ) }}$

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• From identity

$\sf{\red{\boxed{\bold{a^3 + b^3 + 3ab(a+b) = ( a + b)^3}}}}$

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$\sf:\implies\:{\bold{ ( 3 + 5a)^3 }}$

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