Question

phan tich đa thức thanh nhan tử

\(4\text{a}^2b^2-\left(\text{a}^2+b^2-c^2\right)^2\)

Answer 1

Ta có: 4a²b² -(a²+b² -c²)² =[2ab-(a²+b²-c²)][2ab+a²+b²-c²]
=[c²-(a-b)²][(a+b)²-c²]
=(-a+b+c)(a-b+c)(a+b+c)(a+b-c)
Có sai sót nào mong bỏ qua :)

Answer 2

ta có \(4a^2b^4-\left(a^2+b^2-c^2\right)^2\)

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

Theo hằng đẳng thức thứ 3 ta có:

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

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

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

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

=\(2\left(a+b+c\right)2\left(a+b-c\right)\)

=\(\left(2a+2b+2c\right)\left(2a+2b-2c\right)\)