Precalculus Examples

$h^{2} - (a^{2} - 6 a + 9)$

Step 1

Rewrite $a^{2} - 6 a + 9$ as ${(a - 3)}^{2}$ .

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$h^{2} - (a^{2} - 6 a + 3^{2})$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 a = 2 \cdot a \cdot 3$

Step 1.3

Rewrite the polynomial.

$h^{2} - (a^{2} - 2 \cdot a \cdot 3 + 3^{2})$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = a$ and $b = 3$ .

$h^{2} - {(a - 3)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = h$ and $b = a - 3$ .

$(h + a - 3) (h - (a - 3))$

Step 3

Simplify.

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Step 3.1

Apply the distributive property.

$(h + a - 3) (h - a - - 3)$

Step 3.2

Multiply $- 1$ by $- 3$ .

$(h + a - 3) (h - a + 3)$