Question

X³-1 8x³+1 X³+1 125-x³ X³+8y³ 64y³-125x³ 27x³-1/8 A⁶-b³

Answer 1

x^3-1=(x-1)(x^2+x+1)

8x^3+1=(2x+1)(4x^2-2x+1)

x^3+1=(x+1)(x^2-x+1)

125-x^3=(5-x)(25+5x+x^2)

x^3+8y^3=x^3+(2y)^3

=(x+2y)(x^2-2xy+4y^2)

64y^3-125x^3

=(4y)^3-(5x)^3

=(4y-5x)(16y^2+20xy+25x^2)

\(27x^3-\dfrac{1}{8}=\left(3x\right)^3-\left(\dfrac{1}{2}\right)^3=\left(3x-\dfrac{1}{2}\right)\left(9x^2+\dfrac{3}{2}x+\dfrac{1}{4}\right)\)

\(a^6-b^3=\left(a^2\right)^3-b^3\)

\(=\left(a^2-b\right)\cdot\left(a^4+a^2b+b^2\right)\)