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)

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homozygous. one is homozygous, while two is heterozygous.