Answer
$(x-5+6y)(x-5-6y)$
Work Step by Step
$x^{2}-10x+25-36y^{2}$
To factor the polynomial group the first three terms.
$=(x^{2}-10x+25)-36y^{2}$
$x^{2}-10x+25$ is the perfect square trinomial, so the formula for it can be used here is
$ A^{2}- 2.A.B+B^{2} =(A-B)^{2}$
Using the formula, factor the perfect square trinomial
$x^{2}-2.x.5+5^{2}= (x-5) ^{2}$
$x^{2}-10x+25= (x-5) ^{2}$
$x^{2}-10x+25-36y^{2}$ $ =(x-5)^{2}-36y^{2}$
$ =(x-5)^{2}-(6y)^{2}$
Factor the difference of squares. The factors are the sum and difference of the expressions being squared.
Using the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$
$=(x-5+6y)(x-5-6y)$
