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Algebra. Factor x^3-y^3. x3 − y3 x 3 - y 3. Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 + ab+b2) a 3 - b 3 = (a - b) (a 2 + a b + b 2) where a = x a = x and b = y b = y.
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Just like numbers have factors (2×3=6), expressions have factors ((x+2)(x+3)=x^2+5x+6). Factoring is the process...
Solution - Factoring multivariable polynomials. ( x − y) ⋅ ( x 2 + x y + y 2) Step by Step Solution. Step 1 : Trying to factor as a Difference of Cubes: 1.1 Factoring: x3-y3. Theory : A difference of two perfect cubes, a3 - b3 can be factored into. (a-b) • (a2 +ab +b2) Proof : (a-b)• (a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 =
Let $\omega$ be a complex cube root of unity. Then $x^{3} - y^{3} = (x-y)(x- \omega y)(x-\omega^{2}y)$ since both sides vanish when $x \in \{y,\omega y,\omega^{2}y \}$ and the degrees are right.
