4(x-1)^2-9x^2
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a: =(x^2-1)^2-2x(x^2-1)+x(x^2-1)-2x^2
=(x^2-1)(x^2-1-2x)+x(x^2-1-2x)
=(x^2-2x-1)(x^2+x-1)
b: \(=\left(x^2+1\right)^2+x\left(x^2+1\right)+2x\left(x^2+1\right)+2x^2\)
\(=\left(x^2+1\right)\left(x^2+x+1\right)+2x\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x+1\right)^2\cdot\left(x^2+x+1\right)\)
\(=x\left(x^2+2x+1-y^2\right)=x\left[\left(x+1\right)^2-y^2\right]=x\left(x+y+1\right)\left(x-y+1\right)\)
\(=x^2\left(8x-3\right)-\left(8x-3\right)=\left(8x-3\right)\left(x^2-1\right)\)
a) \(=\left(x+y\right)+\left(x+y\right)\left(x-y\right)=\left(x+y\right)\left(1+x-y\right)\)
b) \(=x^2\left(y+1\right)-2y\left(y+1\right)=\left(y+1\right)\left(x^2-2y\right)\)
\(\left(x-4\right)^2=x^2-8x+16\)
\(4x^2-6xy+10x^3=2x\left(2x-3y+5x^2\right)\)
\(=\left(4x-x-1\right)\left(4x+x+1\right)=\left(3x-1\right)\left(5x+1\right)\)
\(=\left(4x-x-1\right)\left(4x+x+1\right)=\left(3x-1\right)\left(5x+1\right)\)
\(x-3\sqrt{x}+2=x-\sqrt{x}-2\sqrt{x}+2=\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)\)
\(x-3\sqrt{x}+2=\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\)
−5𝑥^2−8𝑥+4
\(=\left[2\left(x-1\right)-3x\right]\left[2\left(x-1\right)+3x\right]\\ =\left(2x-2-3x\right)\left(2x-2+3x\right)\\ =\left(-2-x\right)\left(5x-2\right)\\ =\left(x+2\right)\left(2-5x\right)\)