Basic Math Examples

$4 c^{4} + 3 c^{2} y^{2} + y^{4}$

Step 1

Rewrite the middle term.

$4 c^{4} + 2 (2 c^{2}) y^{2} - c^{2} y^{2} + y^{4}$

Step 2

Rearrange terms.

$4 c^{4} + 2 (2 c^{2}) y^{2} + y^{4} - c^{2} y^{2}$

Step 3

Factor first three terms by perfect square rule.

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

Step 4

Rewrite $c^{2} y^{2}$ as ${(c y)}^{2}$ .

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

Step 5

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

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

Step 6

Remove parentheses.

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