Question

phân tích thành nhân tử ( với a , b , x , y là các số không âm )

a) ab + \(b\sqrt{a}\) + \(\sqrt{a}\) + 1

b) \(\sqrt{x^3}\) - \(\sqrt{y^3}\) + \(\sqrt{x^2y}\) - \(\sqrt{xy^2}\)

Answer 1

(a) \(ab+b\sqrt{a}+\sqrt{a}+1\\ =b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\\ =\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

b) \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(x+2\sqrt{xy}+y\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\\ =\left(x-y\right)\left(\sqrt{x}+\sqrt{y}\right)\)

Answer 2

a,\(ab+b\sqrt{a}+\sqrt{a}+1=b\sqrt{a}\left(\sqrt{a}+1\right)+\sqrt{a}+1=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)

b,\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(x+2\sqrt{xy}+y\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)