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\(\text{a)}x\sqrt{x}+\sqrt{x}-x-1\)
\(=\left(x\sqrt{x}+\sqrt{x}\right)-\left(x+1\right)\)
\(=\sqrt{x}\left(x+1\right)-\left(x+1\right)\)
\(=\left(x+1\right)\left(\sqrt{x}-1\right)\)
\(\text{b)}\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)
\(=\left(\sqrt{ab}+2\sqrt{a}\right)+\left(3\sqrt{b}+6\right)\)
\(=\sqrt{a}\left(\sqrt{b}+2\right)+3\left(\sqrt{b}+2\right)\)
\(=\left(\sqrt{b}+2\right)\left(\sqrt{a}+3\right)\)
\(\text{c)}\left(1+\sqrt{x}\right)^2-4\sqrt{x}\)
\(=\left(1+\sqrt{x}\right)^2-\left(2\sqrt{\sqrt{x}}\right)^2\)
\(=\left(1+\sqrt{x}+2\sqrt{\sqrt{x}}\right)\left(1+\sqrt{x}-2\sqrt{\sqrt{x}}\right)\)
\(\text{d)}\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
\(\text{e)}a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\)
\(=\left(a+\sqrt{a}\right)+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\left[\left(\sqrt{a}\right)^2+\sqrt{a}\right]+\left(2\sqrt{ab}+2\sqrt{b}\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\)
\(=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
\(\text{f)}x-2\sqrt{x-1}-a^2\)
\(=\left(\sqrt{x-2}\right)^2\left(\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2}\sqrt{\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}\right)^2-a^2\)
\(=\left(\sqrt{x-2\sqrt{x-1}}+a\right)\left(\sqrt{x-2\sqrt{x-1}}-a\right)\)
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
\(a.x+2\sqrt{x}=\sqrt{x}\left(\sqrt{x}+2\right)\)
\(b.x-\sqrt{x}=\sqrt{x}\left(\sqrt{x}-1\right)\)
\(c.x\sqrt{x}+x-\sqrt{x}-1=x\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)=\left(x-1\right)\left(\sqrt{x}+1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2\)
\(d.a-\sqrt{ab}=\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)\)
\(e.x+2\sqrt{x}+1=\left(\sqrt{x}+1\right)^2=\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)\)
\(f.x-4\sqrt{x}+4=\left(\sqrt{x}-2\right)^2=\left(\sqrt{x}-2\right)\left(\sqrt{x}-2\right)\)
\(g.x-4=\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)\)
\(h.a\sqrt{a}+b\sqrt{b}=\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)\)
\(i.x\sqrt{x}-27=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)\)
\(k.x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
\(j.x^2-\sqrt{x}=\sqrt{x}\left(x\sqrt{x}-1\right)=\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)