Algebra Examples

$1331 x^{3} - 8 y^{3}$

Step 1

Rewrite $1331 x^{3}$ as ${(11 x)}^{3}$ .

${(11 x)}^{3} - 8 y^{3}$

Step 2

Rewrite $8 y^{3}$ as ${(2 y)}^{3}$ .

${(11 x)}^{3} - {(2 y)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 11 x$ and $b = 2 y$ .

$(11 x - (2 y)) ({(11 x)}^{2} + 11 x (2 y) + {(2 y)}^{2})$

Step 4

Simplify.

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Step 4.1

Multiply $2$ by $- 1$ .

$(11 x - 2 y) ({(11 x)}^{2} + 11 x (2 y) + {(2 y)}^{2})$

Step 4.2

Apply the product rule to $11 x$ .

$(11 x - 2 y) (11^{2} x^{2} + 11 x (2 y) + {(2 y)}^{2})$

Step 4.3

Raise $11$ to the power of $2$ .

$(11 x - 2 y) (121 x^{2} + 11 x (2 y) + {(2 y)}^{2})$

Step 4.4

Rewrite using the commutative property of multiplication.

$(11 x - 2 y) (121 x^{2} + 11 \cdot 2 x y + {(2 y)}^{2})$

Step 4.5

Multiply $11$ by $2$ .

$(11 x - 2 y) (121 x^{2} + 22 x y + {(2 y)}^{2})$

Step 4.6

Apply the product rule to $2 y$ .

$(11 x - 2 y) (121 x^{2} + 22 x y + 2^{2} y^{2})$

Step 4.7

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

$(11 x - 2 y) (121 x^{2} + 22 x y + 4 y^{2})$