Answer
$x^{2}$ - 12$x$ + 36 - 49$y^{2}$
= ($x^{2}$ - 12$x$ + 36) - 49$y^{2}$
= ($x$ - 6)$^{2}$ - 49$y^{2}$
= ($x$ - 6)$^{2}$ - (7$y)^{2}$
= ($x$ - 6 + 7$y$)($x$ - 7$y$ - 6)
= ($x$ + 7$y$ - 6)($x$ - 7$y$ - 6)
Work Step by Step
To factor the polynomial, start by grouping the first three terms. Next, you may notice that the first three terms form a perfect square, so the formula for it can be used here (A^2 - 2AB + B^2 = (A - B)^2. After determining the difference of the perfect square, we can use the formula A^2 - B^2 = (A + B)(A - B) to simplify (x-6)^2 and -(7y)^2. Then we can rearrange the last two terms of each trinomial to match the proper order (e.g., x - 6 + 7y = x + 7y - 6).
