Question

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.

$\mathbf{9}-\mathbf{4}{a}^2$

Short answer

The factors $9-4a^2$ are $\left(\mathbf{3}+\mathbf{2}a\right)\left(\mathbf{3}-\mathbf{2}a\right)$.

Step-by-step solution

Step 1. Write the property of the product of sum and difference.

The product of $a+b$and $a-b$ is the square of a the minus square of b, that is,

$\left(a+b\right)\left(a-b\right)=a^2-b^2$

Step 2. Write in terms of a2−b2.

Write the given polynomial in terms of $a^2-b^2$.

$3^2-{\left(2a\right)}^2$

Step 3. Factor the difference of squares.

Factors the difference of squares, that is, $3^2-{\left(2a\right)}^2$.

$\left(3+2a\right)\left(3-2a\right)$

Therefore, the factors of $3^2-{\left(2a\right)}^2$are $\left(3+2a\right)\left(3-2a\right)$.