Question

x-5 over 4x+8 multiply by (12x^2 + 32x + 16) solve without simplifying

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression x-5 over 4x+8 multiplied by (12x^2 + 32x + 16) without simplifying, follow the steps below:

1. Rewrite the expression as (x-5)/(4x+8) * (12x^2 + 32x + 16)
2. Distribute (x-5) into (12x^2 + 32x + 16) to get 12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80
3. Combine like terms to simplify the expression

Therefore, the expression without simplifying is:
12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80.

Answer 2

combine like terms

Answer 3

[AI-generated answer — Bot GPT 3.5]

After distributing (x-5) into (12x^2 + 32x + 16), you will get:

12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80

Next, combine like terms:
12x^3 + (32x^2 - 60x^2) + (16x - 160x) - 80
12x^3 - 28x^2 - 144x - 80

Therefore, the expression without simplifying and combined like terms is:
12x^3 - 28x^2 - 144x - 80.

Answer 4

what happened to that 4x+8 in the denominator?

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for missing the denominator term in the original response. Let's revisit the expression:

The original expression is:
(x-5)/(4x+8) * (12x^2 + 32x + 16)

Distribute (x-5) into (12x^2 + 32x + 16) while keeping the denominator (4x+8) intact:
[(x*12x^2 + x*32x + x*16) - (5*12x^2 + 5*32x + 5*16)] / (4x+8)

This simplifies to:
[(12x^3 + 32x^2 + 16x) - (60x^2 + 160x + 80)] / (4x+8)

Now, let's combine like terms after distributing and simplifying:
12x^3 + 32x^2 + 16x - 60x^2 - 160x - 80

Combine like terms:
12x^3 - 28x^2 - 144x - 80

Therefore, the final expression without simplifying is:
(12x^3 - 28x^2 - 144x - 80) / (4x + 8)