Factorize completely the expression 5x2-8ax-4a2

hello : the factorize completely is : (5x+2a) (x-2a)

Step-by-step explanation:

the first solution:

note : Ax² + Bx + C = A (x - x1) (x - x2) if : Δ ≥ 0 and : Δ = B² - 4AC

x1 = ( - B - √Δ) / 2A x2 = ( - B + √Δ) / 2A

in this execice : A = 5 B = - 8a C = - 4a²

calculate Δ = (-8a) ² - 4 (5) (-4a²) = 64a² + 80a² = 144a² = (12a) ²

x1 = (8a - 12a) / 10 = - 4a/10

x1 = - 2a/5

x2 = (8a + 12a) / 10 = 20a/10

x2 = 2a

put x1 and x2 in expression A (x - x1) (x - x2)

you have : 5 (x + 2a/5) (x - 2a) = (5x+2a) (x-2a)

verify : (5x+2a) (x-2a) = 5x² - 10ax + 2ax - 4a² = 5x² - 8ax - 4a²

the second solution:

5x² - 8ax - 4a² = 5x² + (-10ax + 2ax) - 4a² because

-8ax = -10ax + 2ax

5x² - 8ax - 4a² = (5x² + - 10ax) + (2ax - 4a²)

5x (x - 2a) + 2a (x - 2a) = (x - 2a) (5x+2a)