Algebra Examples

x^{3} y^{3} + z^{3}

$x^{3} y^{3} + z^{3}$

Step 1

Rewrite

x^{3} y^{3}

$x^{3} y^{3}$ as

{(x y)}^{3}

${(x y)}^{3}$ .

{(x y)}^{3} + z^{3}

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

Step 2

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})

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where

a = x y

$a = x y$ and

b = z

$b = z$ .

(x y + z) ({(x y)}^{2} - (x y) z + z^{2})

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

Step 3

Simplify.

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Step 3.1

Apply the product rule to

x y

$x y$ .

(x y + z) (x^{2} y^{2} - (x y) z + z^{2})

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

Step 3.2

Remove parentheses.

(x y + z) (x^{2} y^{2} - x y z + z^{2})

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

(x y + z) (x^{2} y^{2} - x y z + z^{2})

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