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

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

d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)

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

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

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

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

\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)

Lời giải :

\(\sqrt{a-b}-\sqrt{a^2-b^2}\)

\(=\sqrt{a-b}-\sqrt{a-b}\cdot\sqrt{a+b}\)

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

a: \(A=x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}\)

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

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

b: \(B=5x^2-7x\sqrt{y}+2y\)

\(=5x^2-5x\sqrt{y}-2x\sqrt{y}+2y\)

\(=5x\left(x-\sqrt{y}\right)-2\sqrt{y}\left(x-\sqrt{y}\right)\)

\(=\left(x-\sqrt{y}\right)\left(5x-2\sqrt{y}\right)\)

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

\(=\sqrt{ab}\cdot\sqrt{a}+\sqrt{ab}+\sqrt{a}+1\)

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

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

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

a√b + √(ab) + √a + 1

= [a√b + √(ab)] + (√a + 1)

= √(ab)(√a + 1) + (√a + 1)

= (√a + 1)[√(ab) + 1]

a: =(căn a-3)^2-b^2

=(căn a-3-b)(căn a-3+b)

b: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

c: \(x-7\sqrt{x}+12=x-3\sqrt{x}-4\sqrt{x}+12=\left(\sqrt{x}-3\right)\left(\sqrt{x}-4\right)\)

d: x*căn x-64

=(căn x)^3-4^3

=(căn x-4)(x+4căn x+16)

\(a-6\sqrt{a}+9-b^2\\ =\left(\sqrt{a}+3\right)^2-b^2\\ =\left(\sqrt{a}+3-b\right)\left(\sqrt{a}+3+b\right)\)

\(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

\(x-7\sqrt{x}+12\\ =x-4\sqrt{x}-3\sqrt{x}+12\\ =\sqrt{x}\left(\sqrt{x}-4\right)-3\left(\sqrt{x}-4\right)\\ =\left(\sqrt{x}-4\right)\left(\sqrt{x}-3\right)\)

\(x\sqrt{x}+64\\ =\sqrt{x^3}+4^3\\ =\left(\sqrt{x}\right)^3+4^3\\ =\left(\sqrt{x}+4\right)\left(x-4\sqrt{x}+16\right)\)

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

\(=a\left(\sqrt{a}+2\right)+\left(\sqrt{a}+2\right)=\left(\sqrt{a}+2\right)\left(a+1\right)\)

\(a\sqrt{a}+2a+\sqrt{a}+2=a\left(\sqrt{a}+2\right)+\left(\sqrt{a}+2\right)=\left(a+1\right)\left(\sqrt{a}+2\right)\)