Question

Factorise:3-27(a-b)²

Answer 1

$3(1 - 9 {(a - b)}^{2} ) \\ = 3( {1}^{2} - {(3a - 3b)}^{2} ) \\ = 3(1 + 3a - 3b)(1 - 3a + 3b)$

Answer 2

Answer:

$\text{The factorized form is }3(1-3a+3b)(1+3a-3b)$

Step-by-step explanation:

Given the expression

$3-27(a-b)^2$

we have to factorize the above expression.

$3-27(a-b)^2$

Take 3 common from both terms, we get

$3(1-9(a-b)^2)$

$3(1^2-3^2(a-b)^2)$

By the identity

$a^2-b^2=(a-b)(a+b)$

$3(1^2-3(a-b)^2)=3(1-3(a-b))(1+3(a-b))$

$=3(1-3a+3b)(1+3a-3b)$

which is required factorized form.