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a) \(3a-2\sqrt{ab}-b=3a-3\sqrt{ab}+\sqrt{ab}-b\)
\(=3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(3\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
b) \(5a+3\sqrt{ab}-8b=5a-5\sqrt{ab}+8\sqrt{ab}-8b\)
\(=5\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+8\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(5\sqrt{a}+8\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
a) (\(\sqrt{a}-\sqrt{b}\))(3\(\sqrt{a}+b\))
b) \(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
Câu 1 :
a, Ta có : \(A=x-2\sqrt{3}+3\)
\(=x-\sqrt{3}\left(2-\sqrt{3}\right)\)
\(=\left(\sqrt{x}-\sqrt{\sqrt{3}\left(2-\sqrt{3}\right)}\right)\left(\sqrt{x}+\sqrt{\sqrt{3}\left(2-\sqrt{3}\right)}\right)\)
b, Ta có : \(B=x+2\sqrt{x}-3\)
\(=x+2\sqrt{x}+1-4=\left(\sqrt{x}+1\right)^2-4\)
\(=\left(\sqrt{x}+1-2\right)\left(\sqrt{x}+1+2\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)\)
c, Ta có : \(C=x\sqrt{x}-1\)
\(=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
d, Ta có : \(D=2x-3\sqrt{xy}-5y\)
\(=2x+2\sqrt{xy}-5\sqrt{xy}-5y\)
\(=2\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)-5\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(2\sqrt{x}-5\sqrt{y}\right)\)
a, \(7\sqrt{AB}+7B-\sqrt{A}-\sqrt{B}=7\sqrt{B}\left(\sqrt{A}+\sqrt{B}\right)-\left(\sqrt{A}+\sqrt{B}\right)\)\(=\left(\sqrt{A}+\sqrt{B}\right)\left(7\sqrt{B}-1\right)\)
b, \(a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}=\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)+\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{ab}+1\right)\)
c,\(\sqrt{x^2-25y^2}-\sqrt{x-5y}=\sqrt{x-5y}.\sqrt{x+5y}-\sqrt{x-5y}\)
\(=\sqrt{x-5y}\left(\sqrt{x+5y}-1\right)\)
\(a,7\sqrt{AB}+7B-\sqrt{A}-\sqrt{B}\)( Với A>= 0, B>=0)
\(=\left(7\sqrt{AB}-\sqrt{A}\right)+\left(7B-\sqrt{B}\right)\)
\(=7\sqrt{A}\left(\sqrt{B}-1\right)+7\sqrt{B}\left(\sqrt{B}-1\right)\)
\(=\left(\sqrt{B}-1\right)\left(7\sqrt{A}+7\sqrt{B}\right)\)
\(=7\left(\sqrt{B}-1\right)\left(\sqrt{A}+\sqrt{B}\right)\)
\(b,a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\)Với a>= 0, b>=0)
\(=\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)+\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{ab}+1\right)\)
\(c,\sqrt{x^2-25y^2}-\sqrt{x-5y}\)
\(=\sqrt{\left(x-5y\right)\left(x+5y\right)}-\sqrt{x-5y}\)
\(=\sqrt{x-5y}.\sqrt{x+5y}-\sqrt{x-5y}\)
\(=\sqrt{x-5y}\left(\sqrt{x+5y}-1\right)\)
\(a,\)\(7\sqrt{ab}+7b-\sqrt{a}-\sqrt{b}\)
\(=7\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)-\left(\sqrt{a}+\sqrt{b}\right)\)
\(=\left(\sqrt{a}+\sqrt{b}\right)\left(7\sqrt{b}-1\right)\)
\(b,a\sqrt{b}-b\sqrt{a}+\sqrt{a}-\sqrt{b}\)
\(=\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)+\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{ab}-1\right)\)
\(c,\sqrt{x^2-25y^2}-\sqrt{x-5y}\)
\(=\sqrt{\left(x-5y\right)\left(x+5y\right)}-\sqrt{x-5y}\)
\(=\sqrt{x-5y}\left(\sqrt{x-5y}-1\right)\)