Proving Polynomial Identities

To factor the given expression, we will apply the sum of cubes.

a^{3} + b^{3} \Leftrightarrow (a + b) (a^{2} - a b + b^{2})

First, we need to rewrite

512

as

8^{3} .

y^{3} + 512

WritePowWrite as a power

y^{3} + 8^{3}

a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})

(y + 8) (y^{2} - y \cdot 8 + 8^{2})

(- a) b = - a b

(y + 8) (y^{2} - 8 y + 8^{2})

CalcPowCalculate power

(y + 8) (y^{2} - 8 y + 64)

Proving Polynomial Identities 1.10 - Solution