Proving Polynomial Identities

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

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

First we need to rewrite

343

as a cube. Dividing

343

gives

49

and since

49 = 7^{2}

we can write

343 = 7^{3} .

g^{3} - 343

WritePowWrite as a power

g^{3} - 7^{3}

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

(g - 7) (g^{2} + g \cdot 7 + 7^{2})

(g - 7) (g^{2} + 7 g + 7^{2})

CalcPowCalculate power

(g - 7) (g^{2} + 7 g + 49)

Proving Polynomial Identities 1.12 - Solution