Answer: I'll solve A) since there is a lot of work to be shown.
Explanation:
A)
(x−1)³+3x(x−4)+2=x³
Use binomial theorem to expand (x−1)³
x³- 3x² + 3x - 1 + 3x(x-4) + 2=x³
Use distributive property on 3x(x-4)
x³- 3x² + 3x - 1 + 3x²-12x + 2=x³
Add like terms
x³ −9x + 1 =x³
Subtract x³ from both sides.
x³ −9x +1 -x³ = 0
Add x³ and -x³
−9x+1=0
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
−9x=−1
Divide both sides by -9.
x= 1/9