Question

Factorise: $x^2+12x+36$.

• A. $(x+6)(x+2)$
• B. $(x+6)(x+6)$
• C. $(x+4)(x+3)$
• D. $(x+3)(x+12)$

Answer 1

The correct option is B

$(x+6)(x+6)$

The expression $x^2+12x+36$ can be written as,

=$x^2+2\times x\times 6+6^2$.....(i)

Comparing (i) with the identity $a^2+2ab+b^2=(a+b{)}^2$

$a^2=x^2\Rightarrow a=x$.....(ii)

$2ab=2\times x\times 6$

$b^2=6^2\Rightarrow b=6$...(iii)

From (ii) and (iii),

$x^2+12x+36=(x+6{)}^2=(x+6\left)\right(x+6)$

Therefore, the factors of $x^2+12x+36$ are $(x+6)$ and $(x+6)$.