Question

Answer 1

1) \(x^3+1=x^3+1^3=\left(x+1\right)\left(x^2-x+1\right)\)

2) \(x^3+8=x^3+2^3=\left(x+2\right)\left(x^2-2x+4\right)\)

3) \(x^3-8=x^3-2^3=\left(x-2\right)\left(x^2+2x+4\right)\)

4) \(x^3-27=x^3-3^3=\left(x-3\right)\left(x^2+3x+9\right)\)

5) \(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\)

6) \(x^3+8y^3=x^3+\left(2y\right)^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

Answer 2

7) \(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)\)

8) \(x^3-8y^3=x^3-\left(2y\right)^3=\left(x-2y\right)\left(x^2+2xy+4y^2\right)\)

9) \(1+8x^3=1^3+\left(2x\right)^3=\left(1+2x\right)\left(1-2x+4x^2\right)\)

10) \(1+27y^3=1^3+\left(3y\right)^3=\left(1+3y\right)\left(1-3y+9y^2\right)\)

11) \(1-8x^3=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

12) \(27x^3-1=\left(3x\right)^3-1^3=\left(3x-1\right)\left(9x^2+3x+1\right)\)