factor 9x^2+30xy+25y^2 — step-by-step solution

⚠ 9x is read as the product 9*x: for a power, write 9^x‖30xy is read as the product 30*x*y: for a power, write 30^(x*y)‖25y is read as the product 25*y: for a power, write 25^y‖xy is read as the product x*y: for a power, write x^y; for the variable xy, write xy_

The expression:

9 x^{2} + 30 x y + 25 y^{2}

contains several variables so we pick x for factoring

Let's factor in

ℝ

9 x^{2} + 30 x y + 25 y^{2}

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(30 y)}^{2} - 4 \cdot 9 \cdot 25 y^{2}

Δ = {(30 y)}^{2} - 36 \cdot 25 y^{2}

Δ = {(30 y)}^{2} - 900 y^{2}

Δ = 30^{2} \cdot y^{2} - 900 y^{2}

Δ = 900 y^{2} - 900 y^{2}

Δ = 0

Δ = 0

, the equation has one solution:

The unique solution is:

- \frac{b}{2 a}

x = - \frac{30 y}{2 \cdot 9}

x = - \frac{30 y}{18}

x = - \frac{5 y}{3}

▶Factors identified:

9 \cdot {(x + \frac{5 y}{3})}^{2}