Factorize each of the following expression-12 m2-27

12m^2 − 27=3(4m^2 − 9) nbsp; nbsp;[Taken 3 as common]=3[(2m)^2 3^2] nbsp;=3(2m+3)(2m 3) nbsp; nbsp; [∵ a^2 b^2=(a+b)(a b)]Therefore, 12m^2 nbsp; − ...

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Standard VIII

Mathematics

Factorisation by Regrouping Terms

Factorize eac...

Question

Factorize the following expression:
$12 m^{2} - 27$

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Solution

We have
$12 m^{2} - 27$
$= 3 (4 m^{2} - 9)$ [Taken $3$ as common]
$= 3 [(2 m)^{2} - 3^{2}]$
$= 3 (2 m + 3) (2 m - 3)$ [ $∵ a^{2} - b^{2} = (a + b) (a - b)$ ]
Therefore, $12 m^{2} - 27 = 3 (2 m + 3) (2 m - 3)$

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Factorize the following expression:12m2−27

We have12m2−27=3(4m2−9) [Taken 3 as common]=3[(2m)2−32] =3(2m+3)(2m−3) [∵a2−b2=(a+b)(a−b)]Therefore, 12m2−27=3(2m+3)(2m−3)

Factorize the following expression:
$12 m^{2} - 27$

We have
$12 m^{2} - 27$
$= 3 (4 m^{2} - 9)$ [Taken $3$ as common]
$= 3 [(2 m)^{2} - 3^{2}]$
$= 3 (2 m + 3) (2 m - 3)$ [ $∵ a^{2} - b^{2} = (a + b) (a - b)$ ]
Therefore, $12 m^{2} - 27 = 3 (2 m + 3) (2 m - 3)$