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

2 Answers
Apr 6, 2018

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.


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.

Apr 6, 2018

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!