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

2 Answers
Apr 6, 2018

Answer:

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

Answer:

#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#!