Question

Phân tích đa thức sau thành nhân tử:

\(4a^2b^2-\left(a^2+b^2-1\right)^2\)

Answer 1

\(4a^2b^2-\left(a^2+b^2-1\right)^2\)

\(=\left[2ab-\left(a^2+b^2-1\right)\right].\left[2ab+\left(a^2+b^2-1\right)\right]\)

\(=\left(2ab-a^2-b^2+1\right)\left(2ab+a^2+b^2+-1\right)\)

\(=\left[1-\left(a-b\right)^2\right]\left[\left(a+b\right)^2-1\right]\)

\(=\left(1-a+b\right)\left(1+a-b\right)\left(a+b+1\right)\left(a+b-1\right)\)

Answer 2

\(4a^2b^2-\left(a^2+b^2-1\right)^2=\left(2ab+a^2+b^2-1\right)\left(2ab-a^2-b^2+1\right)\)

\(=\left[\left(a+b\right)^2-1\right]\left[1-\left(a-b\right)^2\right]\)

\(=\left(a+b-1\right)\left(a+b+1\right)\left(1+a-b\right)\left(1-a+b\right)\)