Question

Factorize the following expression

$a^2+4b^2+36-4ab+24b-12a$

• A. $(a-2b-6{)}^2$
• B. $(a+2b-6{)}^2$
• C. $(a-2b+6{)}^2$
• D. None of these

Answer 1

The correct option is A $(a-2b-6{)}^2$

$a^2+4b^2+3b-4ab+24b-12a$

Identity

$(A+B+C{)}^2=A^2+B^2+C^2+2AB+2BC+2CA$

$=a^2+(2b{)}^2+(b{)}^2-2\left(a\right)\left(2b\right)+2\left(2b\right)\left(b\right)-2\left(a\right)6$

on comparing

$=(a-2b-6{)}^2$ Ans

Since only (b)Terms constant in $2\left(2b\right)!$ are Positive