Question

Factor completely x^2 - 81

Answer 1

Use the sum-product pattern

2
−
8
1
x
2
−
81
x2−81

2
+
9

−
9

−
8
1

Answer 2

Factor $x^2-81$ by using the difference of two squares.

$x^2-y^2=(x+y)(x-y)$

Our x is x

Our y is 9 (As y² = 81, therefore a single y would be 9)

$(x+9)(x-9)$

Thus, the final answer is (x+9)(x-9)