factor x^2-8xy-20y^2 — step-by-step solution

⚠ xy is read as the product x*y because x and y appear separately

The expression:

x^{2} - 8 x y - 20 y^{2}

contains several variables so we pick x for factorization

Let's factor in

ℝ

x^{2} - 8 x y - 20 y^{2}

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-8 y)}^{2} - 4 \cdot 1 \cdot (- 20 y^{2})

Δ = {(8 y)}^{2} - 4 \cdot (-20) y^{2}

Δ = {(8 y)}^{2} + 80 y^{2}

Δ = 8^{2} \cdot y^{2} + 80 y^{2}

Δ = 64 y^{2} + 80 y^{2}

Δ = 144 y^{2}

The discriminant is a square:

Δ = {(12 y)}^{2}

. With

q = 12 y

, the roots are

\frac{- b - q}{2 a}

and

\frac{- b + q}{2 a}

, including when q is 0

x1 = \frac{- (-8 y) - 12 y}{2}

x1 = \frac{8 y - 12 y}{2}

x1 = \frac{-4 y}{2}

x1 = - \frac{4 y}{2}

x1 = - 2 y

x2 = \frac{- (-8 y) + 12 y}{2}

x2 = \frac{8 y + 12 y}{2}

x2 = \frac{20 y}{2}

x2 = 10 y

▶Factors found:

(x + 2 y) \cdot (x - 10 y)