Question

_Phân tích thành nhân tử :

a) a\(\sqrt{b}-b\sqrt{a}\)

b) \(x\sqrt{x}+\sqrt{x}-x-1\)

c) \(\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)

d) \(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)

Answer 1

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

b,\(x\sqrt{x}+\sqrt{x}-x-1\)

=\(\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)-\(\sqrt{x}\left(\sqrt{x}-1\right)\)

=\(\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1-\sqrt{x}\right)\)

=\(\left(\sqrt{x}-1\right)\left(x+1\right)\)

c,\(\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)=\(\sqrt{a}\left(\sqrt{b}+2\right)\)+\(3\left(\sqrt{b}+2\right)\)

=\(\left(\sqrt{b}+2\right)\left(3+\sqrt{a}\right)\)

d,\(\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}\)

=\(\sqrt{a}\left(\sqrt{x}-\sqrt{y}\right)+\sqrt{b}\left(\sqrt{x}-\sqrt{y}\right)\)

=\(\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{a}+\sqrt{b}\right)\)