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\(x\sqrt{x}+4x-12\sqrt{x}-27\)
\(=\left(x\sqrt{x}-27\right)+\left(4x-12\sqrt{x}\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)+4\sqrt{x}\left(\sqrt{x}-3\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9+4\sqrt{x}\right)\)
\(=\left(\sqrt{x}-3\right)\left(x+7\sqrt{x}+9\right)\)
a, \(\sqrt{a^2-b^2}-\sqrt{a^3+b^3}\)
\(=\sqrt{\left(a+b\right)\left(a-b\right)}-\sqrt{\left(a+b\right)\left(a^2-ab+b^2\right)}\)
\(=\sqrt{a+b}\left(\sqrt{a-b}-\sqrt{a^2-ab+b^2}\right)\)
\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
a: \(=6-\sqrt{15}+2\sqrt{15}=6+\sqrt{15}\)
b: \(=\left(\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\)
\(=7-2\sqrt{21}+2\sqrt{21}=7\)
c: \(=10+5\sqrt{10}-5\sqrt{10}=10\)
d: \(=22-\sqrt{198}+\sqrt{198}=22\)
a) \(5+\sqrt{10}-\sqrt{5}=\sqrt{5}.\left(\sqrt{5}+\sqrt{2}-1\right)\)
b) ĐK: \(a\ge0\)
\(a-4\sqrt{a}-5=a+\sqrt{a}-5\sqrt{a}-5=\left(\sqrt{a}+1\right)\left(\sqrt{a}-5\right)\)
c) ĐK: \(a\ge0\)
\(a+12\sqrt{a}+32=a+8\sqrt{a}+4\sqrt{a}+32=\left(\sqrt{a}+8\right)\left(\sqrt{a}+4\right)\)
d) ĐK: \(a\ge0\)
\(a-5\sqrt{a}+6=a-2\sqrt{a}-3\sqrt{a}+6=\left(\sqrt{a}-2\right)\left(\sqrt{a}-3\right)\)
mình không biết bạn ơi
a. \(11+2\sqrt{10}=\left(\sqrt{10}+1\right)^2\)
b. \(12-2\sqrt{11}=\left(\sqrt{11}-1\right)^2\)
c.\(23+2\sqrt{22}=\left(\sqrt{22}+1\right)^2\)