Question

b1. phân tích đa thưc thanh nhan tu

1. \(a\sqrt{b}\) - \(b\sqrt{a}\)

2. \(7\sqrt{7}\) + \(3\sqrt{3}\)

3. \(a\sqrt{a}\)- \(b\sqrt{b}\)

4. 1 - \(a\sqrt{a}\)

5. x^{2 - \(\sqrt{x}\)}

6. (\(\sqrt{2}\) +1)² -\(4\sqrt{2}\)

7.(\(\sqrt{5}\) +2)² - \(8\sqrt{5}\)

8. \(5\sqrt{2}\) - \(2\sqrt{5}\)

Answer 1

\(a\sqrt{b}-b\sqrt{a}=\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)

\(7\sqrt{7}+3\sqrt{3}=\left(\sqrt{7}+\sqrt{3}\right)\left(7-\sqrt{21}+3\right)=\left(\sqrt{7}+\sqrt{3}\right)\left(10-\sqrt{21}\right)\)

\(a\sqrt{a}-b\sqrt{b}=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)\)

\(1-a\sqrt{a}=\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)\)

\(x^2-\sqrt{x}=\sqrt{x}\left(x\sqrt{x}-1\right)=\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)

\(\left(\sqrt{2}+1\right)^2-4\sqrt{2}=\left(\sqrt{2}-1\right)^2\)

\(\left(\sqrt{5}+2\right)^2-8\sqrt{5}=\left(\sqrt{5}-2\right)^2\)

2 cái trên đều áp dụng HĐT \(\left(a+b\right)^2-4ab=\left(a-b\right)^2\)

\(5\sqrt{2}-2\sqrt{5}=\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)\)