Answer:
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)
