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\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-2x\sqrt{x+3}-x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=2x\left(x-\sqrt{x+3}\right)-\sqrt{x+3}\left(x-\sqrt{x+3}\right)\)
\(=\left(2x-\sqrt{x+3}\right)\left(x-\sqrt{x+3}\right)\)
\(2x^2-3x\sqrt{x+3}+\left(x+3\right)\)
\(=2x^2-x\sqrt{x+3}-2x\sqrt{x+3}+\left(\sqrt{x+3}\right)^2\)
\(=x\left(2x-\sqrt{x+3}\right)-\sqrt{x+3}\left(2x-\sqrt{x+3}\right)\)
\(=\left(x-\sqrt{x+3}\right)\left(2x-\sqrt{x+3}\right)\)
\(C=x^2\left(x^2+x+1\right)-2x\left(x^2+x+1\right)+3\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-2x+3\right)\)
cái trên thì chịu
cái dưới <=> \(\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{xy}+\sqrt{x}-\sqrt{y}\right)\)
a) \(x-2\sqrt{x-1}-a^2=\left(x-1\right)-2\sqrt{x-1}+1-a^2=\left(\sqrt{x-1}-1\right)^2-a^2=\left(\sqrt{x-1}-a-1\right)\left(\sqrt{x-1}+a-1\right)\)
b) \(x\sqrt{x}+y\sqrt{y}+x-y=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)+\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}\right)\)
\(4\left(1+x\right)\left(1+y\right)\left(1+x+y\right)-3x^2y^2=4\left(1+x+y+xy\right)\left(1+x+y\right)-3x^2y^2\)
\(=4\left(1+x+y\right)^2+4xy\left(1+x+y\right)+x^2y^2-4x^2y^2\)
\(=\left[2\left(1+x+y\right)+xy\right]^2-\left(2xy\right)^2=\left(2+2x+2y+xy-2xy\right)\left(2+2x+2y+xy+2xy\right)\)
\(=\left(2+2x+2y-xy\right)\left(2+2x+2y+3xy\right)\)
giúp mình câu khác được ko? câu này mình biết làm òi