Question

Which expression represents x2−12x+36 in factored form?

Answer 1

The factored form of given is:

$x^2 - 12x + 36 = (x-6)(x-6)$

Solution:

Given that,

$x^2 - 12x + 36$

We have to find the factored form

From given,

$x^2-12x+36\\\\\mathrm{Rewrite\:}36\mathrm{\:as\:}6^2\\\\x^2-12x+6^2\\\\\mathrm{Rewrite\:}12x\mathrm{\:as\:}2x\cdot \:6\\\\x^2-2x\cdot \:6+6^2\\\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\\\a=x,\:b=6\\\\Therefore,\\\\x^2-12x+36 = \left(x-6\right)^2\\\\Which\ is\\\\x^2-12x+36 = (x - 6)(x - 6)$

Thus the given expression is factored