Factor 4c^4+3c^2y^2+y^4

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

Rewrite the middle term.

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

Rearrange terms.

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

Factor first three terms by perfect square rule.

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

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

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

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 $b = c y$ .

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

Remove parentheses.

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

Factor 4c^4+3c^2y^2+y^4

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