Factor by Grouping 64x^4+xy^3

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

Factor out the GCF of $x$ from $64 x^{4} + x y^{3}$ .

Factor out the GCF of $x$ from each term in the polynomial.

Factor out the GCF of $x$ from the expression $64 x^{4}$ .

$x (64 x^{3}) + x y^{3}$

Factor out the GCF of $x$ from the expression $x y^{3}$ .

$x (64 x^{3}) + x (y^{3})$

Since all the terms share a common factor of $x$ , it can be factored out of each term.

$x (64 x^{3} + y^{3})$

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

$x ({(4 x)}^{3} + y^{3})$

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 $a = 4 x$ and $b = y$ .

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

Simplify.

Apply the product rule to $4 x$ .

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

Raise $4$ to the power of $2$ .

$x ((4 x + y) (16 x^{2} - 4 x y + y^{2}))$

Multiply $4$ by $- 1$ .

$x ((4 x + y) (16 x^{2} - 4 x y + y^{2}))$

Factor by Grouping 64x^4+xy^3

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