Basic Math Examples

$256 w^{4} - 288 w^{2} y^{2} + 81 y^{4}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $256 w^{4}$ as ${(16 w^{2})}^{2}$ .

${(16 w^{2})}^{2} - 288 w^{2} y^{2} + 81 y^{4}$

Step 1.2

Rewrite $81 y^{4}$ as ${(9 y^{2})}^{2}$ .

${(16 w^{2})}^{2} - 288 w^{2} y^{2} + {(9 y^{2})}^{2}$

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.

$288 w^{2} y^{2} = 2 \cdot (16 w^{2}) \cdot (9 y^{2})$

Step 1.4

Rewrite the polynomial.

${(16 w^{2})}^{2} - 2 \cdot (16 w^{2}) \cdot (9 y^{2}) + {(9 y^{2})}^{2}$

Step 1.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 16 w^{2}$ and $b = 9 y^{2}$ .

${(16 w^{2} - 9 y^{2})}^{2}$

Step 2

Rewrite $16 w^{2}$ as ${(4 w)}^{2}$ .

${({(4 w)}^{2} - 9 y^{2})}^{2}$

Step 3

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

${({(4 w)}^{2} - {(3 y)}^{2})}^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 w$ and $b = 3 y$ .

${((4 w + 3 y) (4 w - (3 y)))}^{2}$

Step 5

Multiply $3$ by $- 1$ .

${((4 w + 3 y) (4 w - 3 y))}^{2}$

Step 6

Apply the product rule to $(4 w + 3 y) (4 w - 3 y)$ .

${(4 w + 3 y)}^{2} {(4 w - 3 y)}^{2}$