Question

Phân tích đa thức thành nhân tử

9(a+b)²-4(a-2b)²

Answer 1

\(9\left(a+b\right)^2-4\left(a-2b\right)^2\)

\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)

\(=\left(3a+3b+2a-4b\right)\left(3a+3b-2a+4b\right)\)

\(=\left(5a-b\right)\left(a+7b\right)\)

Answer 2

\(9\left(a+b\right)^2-4\left(a-2b\right)^2\)

\(=\left[3\left(a+b\right)\right]^2-\left[2\left(a-2b\right)\right]^2\)

\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)

\(=\left(3a+3b+2a-4b\right)\left(3a+3b-2a+4b\right)\)

\(=\left(5a-b\right)\left(a+7b\right)\)