### Home > INT3 > Chapter Ch12 > Lesson 12.1.1 > Problem12-6

12-6.

Factor each of the following expressions. Note that $\sin^2\left(x\right)$ is the notation that is used for $(\sin(x))^2$. Homework Help ✎

1. $\quad x ^ { 2 } - 4$

Remember that a difference of two squares has a special factoring pattern.
$a^2−b^2=\left(a−b\right)\left(a+b\right)$.

$\left(x + 2\right)\left(x − 2\right)$

1. $\quad y ^ { 2 } - 81$

Use the same method as part (a).

1. $1 - x ^ { 2 }$

This might look different than the expressions in parts (a) and (b), but you can use the same method to factor it.

$\left(1 − x\right)\left(1 + x\right)$

1. $1 - \operatorname { sin } ^ { 2 } ( x )$

Think of $\sin^2(x)$ as one big variable (like $x^2$).
Then use the same method as part (c) to factor it.