Algebra Examples

$1 + 9 x^{4} + 6 x^{2}$

Step 1

Rearrange terms.

$1 + 6 x^{2} + 9 x^{4}$

Step 2

Rewrite $1$ as $1^{2}$ .

$1^{2} + 6 x^{2} + 9 x^{4}$

Step 3

Rewrite $9 x^{4}$ as ${(3 x^{2})}^{2}$ .

$1^{2} + 6 x^{2} + {(3 x^{2})}^{2}$

Step 4

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

$6 x^{2} = 2 \cdot 1 \cdot (3 x^{2})$

Step 5

Rewrite the polynomial.

$1^{2} + 2 \cdot 1 \cdot (3 x^{2}) + {(3 x^{2})}^{2}$

Step 6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 1$ and $b = 3 x^{2}$ .

${(1 + 3 x^{2})}^{2}$