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a) \(\sqrt{a^3}-\sqrt{b^3}+\sqrt{a^2b}-\sqrt{ab^2}\)
\(=a\sqrt{a}-b\sqrt{b}+a\sqrt{b}-b\sqrt{a}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)-\left(\sqrt{a}-\sqrt{b}\right)\sqrt{ab}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b-\sqrt{ab}\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+b\right)\)
b) \(x-y+\sqrt{xy^2}-\sqrt{y^3}\)
\(=\left(x-y\right)+\left(y\sqrt{x}-y\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)+y\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}+y\right)\)
\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
a) \(=9x-9\sqrt{xy}+4\sqrt{xy}-4y\)
\(=\left(9x-9\sqrt{xy}\right)+\left(4\sqrt{xy}-4y\right)\)
\(=9\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)+4\sqrt{y}\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(9\sqrt{x}+4\sqrt{y}\right)\)
b)\(=\left(xy+\sqrt{x}.y\right)+\left(\sqrt{x}+1\right)\)
\(=\sqrt{x}y\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)\)
\(=\left(\sqrt{x}+1\right)\left(\sqrt{x}.y+1\right)\)
a,\(x\sqrt{y}+y\sqrt{x}=\sqrt{x}\sqrt{y}.\left(\sqrt{x}+\sqrt{y}\right).\)
c,\(\sqrt{a}-a^2=\sqrt{a}.\left(1-a\sqrt{a}\right)\)
d,\(x-5\sqrt{x}+6=x-3\sqrt{x}-2\sqrt{x}+6\)
\(=\sqrt{x}.\left(\sqrt{x}-3\right)-2.\left(\sqrt{x}-3\right)\)\(=\left(\sqrt{x}-3\right).\left(\sqrt{x}-2\right)\)
1) \(x\sqrt{x}+y\sqrt{y}=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
2) \(x-3=\left(\sqrt{x}-\sqrt{3}\right)\left(\sqrt{x}+\sqrt{3}\right)\)
3) \(a+b=a-\left(-b\right)=\left(\sqrt{a}-\sqrt{-b}\right)\left(\sqrt{a}+\sqrt{-b}\right)\)
p/s: chúc bạn học tốt
a)\(3-\sqrt{3}+\sqrt{15}-3\sqrt{5}=\sqrt{3}\left(\sqrt{3}-1\right)-\sqrt{15}\left(\sqrt{3}-1\right)=\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{15}\right)=\sqrt{3}\left(\sqrt{3}-1\right)\left(1-\sqrt{5}\right)\)\(\)b)\(\sqrt{1-a}+\sqrt{1-a^2}=\sqrt{1-a}.1+\sqrt{1-a}.\sqrt{1+a}=\sqrt{1-a}\left(\sqrt{1+a}+1\right)\)
c)\(\sqrt{a^3}-\sqrt{b^3}+\sqrt{a^2b}-\sqrt{ab^2}=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)+\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b+\sqrt{ab}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(a+2\sqrt{ab}+b\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)^2\)
a= 98 b=35 c=122 và d=129
a, \(5+\sqrt{5}=\sqrt{5}\left(\sqrt{5}+1\right)\)
b, \(a-2\sqrt{a}=\sqrt{a}\left(\sqrt{a}-2\right)\)
c, \(x-\sqrt{xy}=\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)\)
d, \(x-y-\sqrt{x}-\sqrt{y}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}-1\right)\)