Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 2

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

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

Step 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 $b = y$ .

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

Step 4

Simplify.

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Step 4.1

Apply the product rule to $4 x$ .

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

Step 4.2

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

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

Step 4.3

Multiply $4$ by $- 1$ .

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