Algebra Examples

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

Step 1

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 $a = x$ and $b = y + 3$ .

$(x + y + 3) (x^{2} - x (y + 3) + {(y + 3)}^{2})$

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

$(x + y + 3) (x^{2} - x y - x \cdot 3 + {(y + 3)}^{2})$

Step 2.2

Multiply $3$ by $- 1$ .

$(x + y + 3) (x^{2} - x y - 3 x + {(y + 3)}^{2})$

Step 2.3

Rewrite ${(y + 3)}^{2}$ as $(y + 3) (y + 3)$ .

$(x + y + 3) (x^{2} - x y - 3 x + (y + 3) (y + 3))$

Step 2.4

Expand $(y + 3) (y + 3)$ using the FOIL Method.

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Step 2.4.1

Apply the distributive property.

$(x + y + 3) (x^{2} - x y - 3 x + y (y + 3) + 3 (y + 3))$

Step 2.4.2

Apply the distributive property.

$(x + y + 3) (x^{2} - x y - 3 x + y \cdot y + y \cdot 3 + 3 (y + 3))$

Step 2.4.3

Apply the distributive property.

$(x + y + 3) (x^{2} - x y - 3 x + y \cdot y + y \cdot 3 + 3 y + 3 \cdot 3)$

Step 2.5

Simplify and combine like terms.

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Step 2.5.1

Simplify each term.

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Step 2.5.1.1

Multiply $y$ by $y$ .

$(x + y + 3) (x^{2} - x y - 3 x + y^{2} + y \cdot 3 + 3 y + 3 \cdot 3)$

Step 2.5.1.2

Move $3$ to the left of $y$ .

$(x + y + 3) (x^{2} - x y - 3 x + y^{2} + 3 y + 3 y + 3 \cdot 3)$

Step 2.5.1.3

Multiply $3$ by $3$ .

$(x + y + 3) (x^{2} - x y - 3 x + y^{2} + 3 y + 3 y + 9)$

Step 2.5.2

Add $3 y$ and $3 y$ .

$(x + y + 3) (x^{2} - x y - 3 x + y^{2} + 6 y + 9)$