Question

Answer 1

2A:

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

c: \(\left(3x+y\right)\left(9x^2-3xy+y^2\right)=27x^3+y^3\)

d: \(\left(x^2-\dfrac{xy}{2}\right)\left(x^4+\dfrac{x^3y}{2}+\dfrac{x^2y^2}{4}\right)=x^6-\dfrac{1}{8}x^3y^3\)

Answer 2

1A:

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

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

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

d: \(64x^3-27y^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)

Answer 3

1B:

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

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

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

d: \(27x^3-64y^3=\left(3x-4y\right)\left(9x^2+12xy+16y^2\right)\)