\(a,5\left(2x-4\right)+20=10x-20+20=10x\\ b,\left(x-2\right)\left(2x+1\right)+x\left(1-2x\right)\\=2x^2-4x+x-2+x-2x^2\\ =\left(2x^2-2x^2\right)+\left(-4x+x+x\right)-2\\ =-2x-2\\ c,\left(x+1\right)^3+\left(x-1\right)\left(x^2+x+1\right)\\ =\left(x+1\right)^3+\left(x^3-1\right)\\ =x^3+3x^2+3x+1+x^3-1\\ =\left(x^3+x^3\right)+3x^2+3x+\left(1-1\right)\\ =2x^3+3x^2+3x\)
\(d,\left(x-y\right)^2+2x\left(x+y\right)\\ =x^2-2xy+y^2+2x^2+2xy\\ =\left(x^2+2x^2\right)+\left(-2xy+2xy\right)+y^2\\ =3x^2+y^2\)
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