\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
a) 2a−4b=2(a−2b)2a−4b=2(a−2b)
c) 2ax−2ay+2a=2a(x−y+1)2ax−2ay+2a=2a(x−y+1)
e) 3xy(x−4)−9x(4−x)=3x(x−4)(y+3)3xy(x−4)−9x(4−x)=3x(x−4)(y+3)
b,d xem lại đề
\(\text{a)}x\sqrt{x}+\sqrt{x}-x-1\)
\(=\left(x\sqrt{x}+\sqrt{x}\right)-\left(x+1\right)\)
\(=\sqrt{x}\left(x+1\right)-\left(x+1\right)\)
\(=\left(x+1\right)\left(\sqrt{x}-1\right)\)
\(\text{b)}\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)
\(=\left(\sqrt{ab}+2\sqrt{a}\right)+\left(3\sqrt{b}+6\right)\)
\(=\sqrt{a}\left(\sqrt{b}+2\right)+3\left(\sqrt{b}+2\right)\)
\(=\left(\sqrt{b}+2\right)\left(\sqrt{a}+3\right)\)
\(\text{c)}\left(1+\sqrt{x}\right)^2-4\sqrt{x}\)
\(=\left(1+\sqrt{x}\right)^2-\left(2\sqrt{\sqrt{x}}\right)^2\)
\(=\left(1+\sqrt{x}+2\sqrt{\sqrt{x}}\right)\left(1+\sqrt{x}-2\sqrt{\sqrt{x}}\right)\)
\(\text{d)}\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
\(\text{e)}a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\)
\(=\left(a+\sqrt{a}\right)+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\left[\left(\sqrt{a}\right)^2+\sqrt{a}\right]+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
\(\text{f)}x-2\sqrt{x-1}-a^2\)
\(=\left(\sqrt{x-2}\right)^2\left(\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2}\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}+a\right)\left(\sqrt{x-2\sqrt{x-1}}-a\right)\)
\(ab+b\sqrt{a}+\sqrt{a}+1\)
(đk: \(a\ge0\))
\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\sqrt{a}+1=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
ĐK: \(x,y\ge0\)
\(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}=x\left(\sqrt{x}+\sqrt{y}\right)-y\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(x-y\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)^2\left(\sqrt{x}-\sqrt{y}\right)\)
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) \(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
a/\(\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b/ \(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
a) (\(\sqrt{a}-\sqrt{b}\))(\(3\sqrt{a}+\sqrt{b}\))
b) (\(\sqrt{a}-\sqrt{b}\))(5\(\sqrt{a}+8\sqrt{b}\))
a)\(\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{b}+3\sqrt{a}\right)\)
b)\(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
a) \(\left(3\sqrt{a}+b\right)\left(\sqrt{a}-\sqrt{b}\right)\)
b) \(\left(5\sqrt{a}+8\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
a) \(\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b) \(\left(5\sqrt{a}+8\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
a) 3a - 2\(\sqrt{ab}\) - b= 2a + a - 2\(\sqrt{ab}\) - b = 2\(\sqrt{a}\)( \(\sqrt{a}\) - \(\sqrt{b}\) ) +(a - b )
=2\(\sqrt{a}\)( \(\sqrt{a}\) - \(\sqrt{b}\) )+(\(\sqrt{a}\) +\(\sqrt{b}\))(\(\sqrt{a}\) -\(\sqrt{b}\))= (\(\sqrt{a}\) -\(\sqrt{b}\))( 2\(\sqrt{a}\) +\(\sqrt{a}\) +\(\sqrt{b}\))=(\(\sqrt{a}\) -\(\sqrt{b}\))(3\(\sqrt{a}\) +\(\sqrt{b}\) )
b) 5a +3\(\sqrt{ab}\) - 8b= 5a + 8\(\sqrt{ab}\) - 5\(\sqrt{ab}\) - 8b= 5\(\sqrt{a}\)(\(\sqrt{a}\) - \(\sqrt{b}\)) +8\(\sqrt{b}\)( \(\sqrt{a}\) - \(\sqrt{b}\))
=(\(\sqrt{a}\) - \(\sqrt{b}\))(5\(\sqrt[]{a}\) +8\(\sqrt{b}\))
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.\(5a+3\sqrt{ab}-8b=5a-5\sqrt{ab}+8\sqrt{ab}-8b=5\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+8\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(5\sqrt{a}+8\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
bài 3 e gửi thiếu nên e gửi vào đây luôn
a) \(3a-2\sqrt{ab}-b=\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b) \(5a+3\sqrt{ab}-8b=\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
a)\(3a-2\sqrt{ab}-b=3a-3\sqrt{ab}+\sqrt{ab}-b=\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b)\(5a+3\sqrt{ab}-8b=5a-5\sqrt{ab}+8\sqrt{ab}-8b=\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
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(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)3a−2ab−b=3a−3ab+ab−b=3a(a−b)+b(a−b)=(a−b)(3a+b)
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(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)5a+3ab−8b=5a−5ab
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a) \(\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b) \(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+\sqrt{b}\right)\)
a) \(\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b) \(\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
a) \(3a-2\sqrt{ab}-b=3a-3\sqrt{ab}+\sqrt{ab}-b=3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b) \(5a+3\sqrt{ab}-8b=5a-5\sqrt{ab}+8\sqrt{ab}-8b=5\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+8\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt[]{a}+8\sqrt{b}\right)\)
a)3a-2√ab-b=3a-3√ab+√ab-b
=3√a.(√a-√b)+√b.(√a-√b)
=(3√a+√b).(√a-√b)
b)5a+3√ab-8b
=5a-5√ab+8√ab-8b
=5√a.(√a-√b)+8√b.(√a-√b)
=(√a-√b).(5√a+8√b)
a,,\(3a-2\sqrt{ab}-b=3\sqrt{a}^2-3\sqrt{ab}+\sqrt{ab}-\sqrt{b}^2=3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)=\left(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)\)
b,
\(5a+3\sqrt{ab}-8b=5\sqrt{a}^2-5\sqrt{ab}+8\sqrt{ab}-8b=\left(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)\)
\(b.=5a+3\sqrt{a}\sqrt{b}-8b\\ \\ \\ =5a+8\sqrt{a}\sqrt{b}-5\sqrt{a}\sqrt{b}-8b=\sqrt{a}\left(5\sqrt{a}+8\sqrt{b}\right)-\sqrt{b}\left(5\sqrt{a}+8\sqrt{b}\right)\\ \\ \\ \\ \\ \\ =\left(5\sqrt{a}+8\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)\(a.=3a-2\sqrt{a}\sqrt{b}-b=3a+\sqrt{a}\sqrt{b}-3\sqrt{a}\sqrt{b}-b=\sqrt{a}\left(3\sqrt{a}+\sqrt{b}\right)-\sqrt{b}\left(3\sqrt{a}+\sqrt{b}\right)=\left(3\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)\)
a)3a-2\(\sqrt{ab}\)-b=2a+a-2\(\sqrt{ab}\)-b=(2a-2\(\sqrt{ab}\))+(a-b)=2\(\sqrt{a}\)(\(\sqrt{a}\)-\(\sqrt{b}\))+(a-b)=(\(\sqrt{a}\)-\(\sqrt{b}\))(2\(\sqrt{a}\)+\(\sqrt{a}\)\(\sqrt{b}\))=(\(\sqrt{a}\)-\(\sqrt{b}\))(3\(\sqrt{a}\)+\(\sqrt{b}\))
b)5a+3\(\sqrt{ab}\)-8b=5a+8\(\sqrt{ab}\)-5\(\sqrt{ab}\)-8b=5\(\sqrt{a}\)(\(\sqrt{a}\)-\(\sqrt{b}\))+8\(\sqrt{b}\)(\(\sqrt{a}\)-\(\sqrt{b}\))=(5\(\sqrt{a}\)+8\(\sqrt{b}\))(\(\sqrt{a}\)-\(\sqrt{b}\))
a) 3a - 2\(\sqrt{ab}\) - b
= 3a -3\(\sqrt{ab}\)+\(\sqrt{ab}\)-b
=(\(\sqrt{a}-\sqrt{b}\))(\(3\sqrt{a}+\sqrt{b}\))
b) 5a + \(3\sqrt{ab}\) - 8b
= 5a - 5\(\sqrt{ab}\) + 8\(\sqrt{ab}\) - 8b
= (\(\sqrt{a}-\sqrt{b}\))(5\(\sqrt{a}+8\sqrt{b}\) )
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(\sqrt{a}-\sqrt{b}\right)\left(3\sqrt{a}+\sqrt{b}\right)3a−2ab−b=3a−3ab+ab−b=3a(a−b)+b(a−b)=(a−b)(3a+b)
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(\sqrt{a}-\sqrt{b}\right)\left(5\sqrt{a}+8\sqrt{b}\right)5a+3ab−8b=5a−5ab
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a)=(√a-√b)(3√a+√b)
b)=(√a-√b)(5√a+8√b)