Question

Factor the expression 64a^ 2- 16ab + b^ 2 into a product of binomials

Answer 1

you are supposed to recognize this as
\[(a-b)^2=a^2-2ab+b^2\] with
\[a=4a,b=b\]

Answer 2

64a^ 2- 16ab + b^ 2


64a^ 2 - 8ab - 8ab + b^ 2


(64a^ 2 - 8ab) +(-8ab + b^2)


8a(8a - b) +(-8ab + b^2)


8a(8a - b) - b(8a - b)


(8a - b)(8a - b)


(8a - b)^2


So \[\large 64a^ 2- 16ab + b^ 2 = (8a - b)^2\]