Finite Math Examples

$x^{6} + 2 x^{3} y^{3} + y^{6}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 1.2

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Step 1.3

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

$2 x^{3} y^{3} = 2 \cdot x^{3} \cdot y^{3}$

Step 1.4

Rewrite the polynomial.

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

Step 1.5

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

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

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = y$ .

${((x + y) (x^{2} - x y + y^{2}))}^{2}$

Step 3

Apply the product rule to $(x + y) (x^{2} - x y + y^{2})$ .

${(x + y)}^{2} {(x^{2} - x y + y^{2})}^{2}$