Question

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Answer 1

\(a,\left(x+1\right)^3-x\left(x-2\right)^2-1\\ =\left(x^3+3x^2+3x+1\right)-x\left(x^2-4x+4\right)-1\\ =x^3-x^3+3x^2+4x^2+3x-4x+1-1\\ =7x^2-x\\ ---\\ b,\left(x+1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x^2-x+1\right)\\ =\left[\left(x+1\right)\left(x^2-x+1\right)\right].\left[\left(x-1\right)\left(x^2+x+1\right)\right]=\left(x^3+1\right)\left(x^3-1\right)=x^6-1\\ ---\\ c,\left(2x+1\right)^3=\left(2a\right)^3+3.\left(2a\right)^2.1+3.2a.1^2+1^3=8a^3+12a^2+6a+1\\ d,\left(3a-2b\right)^3=\left(3a\right)^3-3.\left(3a\right)^2.2b+3.3a.\left(2b\right)^2-\left(2b\right)^3\\ =27a^3-54a^2b+36ab^2-8b^3\)