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Maths-

General

Easy

Question

Write the factored form of the given expression.
$3 x cubed minus 12 x squared plus 12 x$

hint Hint:

Take out the greatest common factor of elements then divide the mid term as a product of 1st and 3rd elements and take common elements out.

The correct answer is: 3x (x - 2)2 is the factorized form of given expression.

Ans:- 3x (x - 2)² is the factorized form of given expression.
Given, $3 x cubed minus 12 x squared plus 12 x$
Taking out 3x as common factor we get $3 x open parentheses x squared minus 4 x plus 4 close parentheses$
Write $4 text as end text left parenthesis 2 right parenthesis squared text and end text minus 4 x text as end text minus 2 left parenthesis x right parenthesis left parenthesis 2 right parenthesis text then we get end text 4 open parentheses left parenthesis x right parenthesis squared minus 2 left parenthesis x right parenthesis left parenthesis 2 right parenthesis plus 2 squared close parentheses$
Applying $x squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared text formula here end text a equals x space space semicolon space b equals 2$
We get = $3 x cubed minus 12 x squared plus 12 x equals 3 x left parenthesis x minus 2 right parenthesis squared$ .
∴ 3x (x - 2)² is the factorized form of the given expression.

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