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Maths-

General

Easy

Question

Factor the given expression completely.
$2 x cubed plus 32 x squared plus 128 x$

hint Hint:

using the formula $a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared$ factorize the given expression

The correct answer is: 2x(x+8)2 is the factorized form of the given expression.

Ans:- $2 x left parenthesis x plus 8 right parenthesis squared$ is the factorized form of the given expression.
Given, $2 x cubed plus 32 x squared plus 128 x$
Taking common factor 2x then we get $2 x open parentheses x squared plus 16 x plus 64 close parentheses$
Write $16 x text as end text 2 left parenthesis x right parenthesis 8 text and end text 64 text as end text left parenthesis 8 right parenthesis squared text and we get end text 2 x open square brackets left parenthesis x right parenthesis squared plus 2 left parenthesis x right parenthesis 8 plus 8 squared close square brackets$
Applying $a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared$
Here a = x ; b = 8
We get , $2 x cubed plus 32 x squared plus 128 x equals 2 x left parenthesis x plus 8 right parenthesis squared$
∴ $2 x left parenthesis x plus 8 right parenthesis squared$ is the factorized form of the given expression.

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