Algebra Examples

$48 x^{2} y^{2} + 9 + 64 x^{4} y^{4}$

Step 1

Rearrange terms.

$9 + 48 x^{2} y^{2} + 64 x^{4} y^{4}$

Step 2

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

$3^{2} + 48 x^{2} y^{2} + 64 x^{4} y^{4}$

Step 3

Rewrite $64 x^{4} y^{4}$ as ${(8 x^{2} y^{2})}^{2}$ .

$3^{2} + 48 x^{2} y^{2} + {(8 x^{2} y^{2})}^{2}$

Step 4

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

$48 x^{2} y^{2} = 2 \cdot 3 \cdot (8 x^{2} y^{2})$

Step 5

Rewrite the polynomial.

$3^{2} + 2 \cdot 3 \cdot (8 x^{2} y^{2}) + {(8 x^{2} y^{2})}^{2}$

Step 6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3$ and $b = 8 x^{2} y^{2}$ .

${(3 + 8 x^{2} y^{2})}^{2}$