Question

Phân tích đa thức thành nhân tử:

a) \(a+2\sqrt{ab}+b\)

b) \(x^2+2xy+y^2+x^2-y^2\)

Answer 1

a, \(a+2\sqrt{ab}+b=\left(\sqrt{a}+\sqrt{b}\right)^2\)

Answer 2

b,\(x^2+2xy+y^2+x^2-y^2=\left(x+y\right)^2+\left(x-y\right)\left(x+y\right)\)\(=\left(x+y\right)\left(x+y+x-y\right)=2x\left(x+y\right)\)

Answer 3

a) Ta có: \(a+2\sqrt{ab}+b\)

= \(\sqrt{a}^2+2\sqrt{ab}+\sqrt{b}^2\)

= \(\left(\sqrt{a}+\sqrt{b}\right)^2\)

b) Ta có: \(x^2+2xy+y^2+x^2-y^2\)

= \(\left(x+y\right)^2+\left(x-y\right)\left(x+y\right)\)

= \(\left(x+y\right)\left[\left(x+y\right)+\left(x-y\right)\right]\)

= \(2x\left(x+y\right)\)