Question

How do you simplify `12x (x^2 + 3) - 8x (x^2 + 3) + 5 (x^2 + 3)`?

Answer 1

You can either distribute and combine like terms or you can factor.

Explanation:

I'll show distributing first.

I like to distribute one term at a time then combine them.
`12x(x^2+3)rArr12x^3+36x`
`-8x(x^2+3)rArr-8x^3-24x`
`5(x^2+3)rArr5x^2+15`

`12x^3+36x-8x^3-24x+5x^2+15`

Combine like terms
`4x^3+12x+5x^2+15`

Put it in the proper order
`4x^3+5x^2+12x+15`

That would be it for distributing.

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For factoring, you find a common factor in each term and pull it out.

`12x(x^2+3)-8x(x^2+3)+5(x^2+3)`

Every term is multiplied by `(x^2+3)`. Pulling that out of the expression gives you
`(x^2+3)(12x-8x+5)`

Then combine like terms
`(x^2+3)(4x+5)`

And that's it. I hope this helps.

Answer 2

`4x^3 + 5x^2 + 12x + 15`

Explanation:

• Use the distributive property to simplify each part in parenthesis, then add.

You started with `12x(x^2 + 3) - 8x(x^2 + 3) + 5(x^2 + 3)`

Distribute the 12x, -8x, and 5 to the values in parenthesis they are next to:
`((12x*x^2) + (12x*3)) + ((-8x*x^2) + (-8x*3)) + ((5*x^2) + (5*3))`
`12x^3 + 36x -8x^3 - 24x + 5x^2 + 15`

Rearrange so you can combine like terms (list with exponents in descending order):
`12x^3 -8x^3 + 5x^2 + + 36x - 24x + 15`

Combine like terms:
`4x^3 + 5x^2 + 12x + 15`

• Alternatively, because the value in parenthesis is the same (it is `x^2 + 3`), you can take add the coefficients together and multiply their sum by `x^2 + 3` .

You started with `12x(x^2 + 3) - 8x(x^2 + 3) + 5(x^2 + 3)`

The coefficients are 12x, -8x, and 5. Add those together. You are able to do that because they are each being multiplied by the same thing (`x^2 + 3`).
`12x + (-8x) + 5`

Combine like terms:
`4x + 5`

Multiply the value you just got (`4x + 5`) by the value each coefficient was being multiplied by in the original problem (`x^2 + 3`):
`(4x + 5) * (x^2 + 3)`

Distributive Property (use the FOIL method):
`(4x*x^2) + (4x*3) + (5*x^2) + (5*3)`

Multiply to find each value in parenthesis:
`4x^3 + 12x + 5x^2 + 15`

Rearrange (list with exponents in descending order):
`4x^3 + 5x^2 + 12x + 15`

There are no like terms to combine, so your answer is `4x^3 + 5x^2 + 12x + 15`!