Factor x^(3n)+y^(3n)

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

Step 1

Rewrite $x^{3 n}$ as ${(x^{n})}^{3}$ .

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

Step 2

Rewrite $y^{3 n}$ as ${(y^{n})}^{3}$ .

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

Step 3

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 $a = x^{n}$ and $b = y^{n}$ .

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

Step 4

Simplify.

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

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

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

Move $2$ to the left of $n$ .

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

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

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

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

Move $2$ to the left of $n$ .

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

Factor x^(3n)+y^(3n)

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