Finite Math Examples

$x^{6} - 216 y^{3}$

Step 1

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

${(x^{2})}^{3} - 216 y^{3}$

Step 2

Rewrite $216 y^{3}$ as ${(6 y)}^{3}$ .

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

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 $a = x^{2}$ and $b = 6 y$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Multiply $6$ by $- 1$ .

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

Step 4.2

Multiply the exponents in ${(x^{2})}^{2}$ .

Tap for more steps...

Step 4.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$(x^{2} - 6 y) (x^{2 \cdot 2} + x^{2} (6 y) + {(6 y)}^{2})$

Step 4.2.2

Multiply $2$ by $2$ .

$(x^{2} - 6 y) (x^{4} + x^{2} (6 y) + {(6 y)}^{2})$

Step 4.3

Rewrite using the commutative property of multiplication.

$(x^{2} - 6 y) (x^{4} + 6 x^{2} y + {(6 y)}^{2})$

Step 4.4

Apply the product rule to $6 y$ .

$(x^{2} - 6 y) (x^{4} + 6 x^{2} y + 6^{2} y^{2})$

Step 4.5

Raise $6$ to the power of $2$ .

$(x^{2} - 6 y) (x^{4} + 6 x^{2} y + 36 y^{2})$