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\(a\sqrt{a}+2a+\sqrt{a}+2=\left(a\sqrt{a}+2a\right)+\left(\sqrt{a}+2\right)\)
\(=a\left(\sqrt{a}+2\right)+\left(\sqrt{a}+2\right)=\left(\sqrt{a}+2\right)\left(a+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(ab+b\sqrt{a}+\sqrt{a}+1=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
\(=b\sqrt{a}\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(b\sqrt{a}+1\right)\)
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\(a,x-3\sqrt{x}+2\)
\(=x-3\sqrt{x}+\frac{9}{4}-\frac{1}{4}\)
\(=\left(x-\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^2=\left(x+2\right)\left(x-2\right)\)
câu a mình nhìn nhầm :
\(=\left(x-1\right)\left(x+2\right)\)
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\(a\sqrt{b}+\sqrt{ab}+\sqrt{a}+1\)
\(=\sqrt{ab}\cdot\sqrt{a}+\sqrt{ab}+\sqrt{a}+1\)
\(=\left(\sqrt{ab}\cdot\sqrt{a}+\sqrt{ab}\right)+\left(\sqrt{a}+1\right)\)
\(=\sqrt{ab}\cdot\left(\sqrt{a}+1\right)+\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{ab}+1\right)\left(\sqrt{a}+1\right)\)
a√b + √(ab) + √a + 1
= [a√b + √(ab)] + (√a + 1)
= √(ab)(√a + 1) + (√a + 1)
= (√a + 1)[√(ab) + 1]
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a,\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)=\sqrt{a}\left(\sqrt{b-1}\right)-\left(\sqrt{b}-1\right)=\left(\sqrt{a}-1\right).\left(\sqrt{b}-1\right).\)
mầy phần này dễ mà mình gại đánh máy quá
những phần sau sử dụng hằng đẳng thức nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5\sqrt{14}-\sqrt{21}=\sqrt{7}\left(5\sqrt{2}-\sqrt{3}\right)\)