Đề bài: Phân tích đa thức thành nhân tử:
1. a - 3\(\sqrt{a}\) + 2
2. a + 4\(\sqrt{a}\) + 3
3. a\(\sqrt{a}\) - 26\(\sqrt{b}\) - 36\(\sqrt{a}\)
4. \(\sqrt{x^3}\) - \(\sqrt{y^3}\) + \(\sqrt{x^2y}\) - \(\sqrt{xy^2}\)
5. \(\sqrt{a^3b}\) + \(\sqrt{ab^3}\) + \(\sqrt{\left(a+b\right)^2}\)
6. x + y - 9 - 2 \(\sqrt{xy}\)
Các bạn giúp tớ vs ạ, tớ cảm ơn!!!!!
3. :))
4. \(\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}\)
\(=x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}\)
\(=\sqrt{x}\left(x-y\right)+\sqrt{y}\left(x-y\right)\)
\(=\left(x-y\right)\left(\sqrt{x}+\sqrt{y}\right)\)
5. \(\sqrt{a^3b}+\sqrt{ab^3}+\sqrt{\left(a+b\right)^2}\)
\(=a\sqrt{ab}+b\sqrt{ab}+\sqrt{a+b}\cdot\sqrt{a+b}\)
\(=\sqrt{ab}\cdot\left(a+b\right)+\sqrt{a+b}\cdot\sqrt{a+b}\)
\(=\sqrt{ab}\cdot\sqrt{\left(a+b\right)^2}+\sqrt{\left(a+b\right)^2}\)
\(=\left|a+b\right|\left(\sqrt{ab}+1\right)\)
1. \(a-3\sqrt{a}+2=a-\sqrt{a}-2\sqrt{a}+2=\sqrt{a}\left(\sqrt{a}-1\right)-2\left(\sqrt{a}-1\right)\)
\(=\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)\)
2. \(a+4\sqrt{a}+3=a+3\sqrt{a}+\sqrt{a}+3=\sqrt{a}\left(\sqrt{a}+3\right)+\left(\sqrt{a}+3\right)\)
\(=\left(\sqrt{a}+3\right)\left(\sqrt{a}+1\right)\)
6. \(x+y-9-2\sqrt{xy}\)
\(=\left(x-2\sqrt{xy}+y\right)-9\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2-3^2\)
\(=\left(\sqrt{x}-\sqrt{y}-3\right)\left(\sqrt{x}-\sqrt{y}+3\right)\)
Câu 3 sau khi sửa lại đề: \(a\sqrt{a}-3b\sqrt{a}-2b\sqrt{b}\)
\(=a\sqrt{a}-b\sqrt{a}-2b\sqrt{a}-2b\sqrt{b}\)
\(=\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)-2b\left(\sqrt{a}+\sqrt{b}\right)\)
\(=\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}-2b\right)\)
Lạ nhỉ! Câu 3 tự nhiên lòi ra thak b là sao ta??! :D