Basic Math Examples

$y^{6} - 125$

Step 1

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

${(y^{2})}^{3} - 125$

Step 2

Rewrite $125$ as $5^{3}$ .

${(y^{2})}^{3} - 5^{3}$

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 $a = y^{2}$ and $b = 5$ .

$(y^{2} - 5) ({(y^{2})}^{2} + y^{2} \cdot 5 + 5^{2})$

Step 4

Simplify.

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Step 4.1

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

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Step 4.1.1

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

$(y^{2} - 5) (y^{2 \cdot 2} + y^{2} \cdot 5 + 5^{2})$

Step 4.1.2

Multiply $2$ by $2$ .

$(y^{2} - 5) (y^{4} + y^{2} \cdot 5 + 5^{2})$

Step 4.2

Move $5$ to the left of $y^{2}$ .

$(y^{2} - 5) (y^{4} + 5 y^{2} + 5^{2})$

Step 4.3

Raise $5$ to the power of $2$ .

$(y^{2} - 5) (y^{4} + 5 y^{2} + 25)$