Question

50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!

Answer 1

D.
`8a^(9) -4a^(3) +1`

Explanation:

Given
`r(x)=x^(3) -2x+1` and find
`r(2a^(3) )` :

• 
  `r(2a^(3) )` is the same as saying
  `x=2a^(3)`
• So, we have
  `r(2a^(3) )=(2a^(3))^(3) -2(2a^(3))+1`

Solve for
`r(2a^(3) )` :

1.
`r(2a^(3) )=(2a^(3))^(3) -2(2a^(3))+1`

• Start with simplifying
  `(2a^(3))^(3)`
• 
  `(2a^(3))^(3)=2^(3)*(a^(3))^(3)=8*a^(3*3)=8a^(9)`
• When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.
• When you multiply two terms that are raised to a power, you add the powers.
• When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.
• When you have a power raised to a power, you multiply the powers.

2.
`r(2a^(3) )=8a^(9) -2(2a^(3))+1`

• Simplify
  `2(2a^(3))`
• Multiply two times the quantity
• 
  `2(2a^(3))=4a^(3)`

3.
`r(2a^(3) )=8a^(9) -4a^(3)+1`

Answer:

So, if
`r(x)=x^(3) -2x+1`, then
`r(2a^(3) )=(2a^(3))^(3) -2(2a^(3))+1=8a^(9) -4a^(3)+1`.

Then the answer is D.
`r(2a^(3) )=8a^(9) -4a^(3)+1`

Answer 2

D

Explanation: