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

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.
$12 x \left({x}^{2} + 3\right) \Rightarrow 12 {x}^{3} + 36 x$
$- 8 x \left({x}^{2} + 3\right) \Rightarrow - 8 {x}^{3} - 24 x$
$5 \left({x}^{2} + 3\right) \Rightarrow 5 {x}^{2} + 15$

$12 {x}^{3} + 36 x - 8 {x}^{3} - 24 x + 5 {x}^{2} + 15$

Combine like terms
$4 {x}^{3} + 12 x + 5 {x}^{2} + 15$

Put it in the proper order
$4 {x}^{3} + 5 {x}^{2} + 12 x + 15$

That would be it for distributing.

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

$12 x \left({x}^{2} + 3\right) - 8 x \left({x}^{2} + 3\right) + 5 \left({x}^{2} + 3\right)$

Every term is multiplied by $\left({x}^{2} + 3\right)$. Pulling that out of the expression gives you
$\left({x}^{2} + 3\right) \left(12 x - 8 x + 5\right)$

Then combine like terms
$\left({x}^{2} + 3\right) \left(4 x + 5\right)$

And that's it. I hope this helps.

Apr 6, 2018

$4 {x}^{3} + 5 {x}^{2} + 12 x + 15$

#### Explanation:

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

You started with $12 x \left({x}^{2} + 3\right) - 8 x \left({x}^{2} + 3\right) + 5 \left({x}^{2} + 3\right)$

Distribute the 12x, -8x, and 5 to the values in parenthesis they are next to:
$\left(\left(12 x \cdot {x}^{2}\right) + \left(12 x \cdot 3\right)\right) + \left(\left(- 8 x \cdot {x}^{2}\right) + \left(- 8 x \cdot 3\right)\right) + \left(\left(5 \cdot {x}^{2}\right) + \left(5 \cdot 3\right)\right)$
$12 {x}^{3} + 36 x - 8 {x}^{3} - 24 x + 5 {x}^{2} + 15$

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

Combine like terms:
$4 {x}^{3} + 5 {x}^{2} + 12 x + 15$

• 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 $12 x \left({x}^{2} + 3\right) - 8 x \left({x}^{2} + 3\right) + 5 \left({x}^{2} + 3\right)$

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 (${x}^{2} + 3$).
$12 x + \left(- 8 x\right) + 5$

Combine like terms:
$4 x + 5$

Multiply the value you just got ($4 x + 5$) by the value each coefficient was being multiplied by in the original problem (${x}^{2} + 3$):
$\left(4 x + 5\right) \cdot \left({x}^{2} + 3\right)$

Distributive Property (use the FOIL method):
$\left(4 x \cdot {x}^{2}\right) + \left(4 x \cdot 3\right) + \left(5 \cdot {x}^{2}\right) + \left(5 \cdot 3\right)$

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

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

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