To rewrite \( 8(x + 1)^3 \), we'll start by expanding the expression.
First, we expand \( (x + 1)^3 \): \[ (x + 1)^3 = (x + 1)(x + 1)(x + 1) \] Using the binomial expansion or applying the distributive property: \[ (x + 1)^3 = x^3 + 3x^2 + 3x + 1 \]
Now, we multiply this by 8: \[ 8(x + 1)^3 = 8(x^3 + 3x^2 + 3x + 1) = 8x^3 + 24x^2 + 24x + 8 \]
The options provided don’t exactly match this expanded form. However, let's examine the choices:
A. \( 8x(x - 1) + (x + 1) + (x + 1) \)
B. \( 8x(x + 1)x(x + 1) \)
C. \( 8 + x^3 + 3 \)
D. \( 8x^3 + 1 \)
None of these options accurately represent \( 8(x + 1)^3 \). The closest correct form to our expansion is having \( 8x^3 \) included, but all the terms are missing or incorrect in the options given.
If you need a correct option based on the expanded form, it would be:
\( 8x^3 + 24x^2 + 24x + 8 \).
Feel free to provide additional context if you need something different!