How do you simplify 12x(x2+3)−8x(x3+3)+5(x2+3)?

Question

How do you simplify   12x(x2+3)−8x(x3+3)+5(x2+3)?

sigcinweq0s · Accepted Answer

Step 1  Ill

utripljigmp · Accepted Answer

Step 1
Use the distributive property to simplify each part in parenthesis, then add.
You started with

12 x (x^{2} + 3) - 8 x (x^{2} + 3) + 5 (x^{2} + 3)

Distribute the 12x, -8x, and 5 to the values in parenthesis they are next to:

((12 x \times x^{2}) + (12 x \times 3)) + ((- 8 x \times x^{2}) + (- 8 x \times 3)) + ((5 \times x^{2}) + (5 \times 3))

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 (x^{2} + 3) - 8 x (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)

12 x + (- 8 x) + 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)

(4 x + 5) \times (x^{2} + 3)

Distributive Property (use the FOIL method):

(4 x \times x^{2}) + (4 x \times 3) + (5 \times x^{2}) + (5 \times 3)

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

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