How to work problem 12p^2 + 8p^2

Question

I want to see the steps how to work this problem.

Answer 1

Hi Felicia! Great question there.

12p² + 8p² = ? 

One of the big ideas in algebra is 'like terms'. You may have seen or heard it. What does it mean? Basically, it comes down to apples and oranges. If you have 12 apples and 8 oranges, what do you have? It's a trick question. You can't really add them. You just have 12 apples and 8 oranges.You could add 3 apples to 8 apples or you could subtract 10 oranges from 18 oranges because they are the same type.

Im algebra we use letters and variables to keep track of types. We can add x's "5x + 3x = 8x" for example. You may have noticed the p^2 in the problem. That means "p squared"' or "p * p". You can add p^2 together just like x's or apples or oranges.

The steps are:

1) look at all the terms in the expression  "12p^2 + 8p^2 

We see there is just one type of term, and that's "p^2"

2) add or subtract the coefficients in front of the terms. A coefficient is thno umber in front of the term. They can be positive or negative. 

Here the coefficients are +12 and + 8

3) Find the sum of all the terms. That is your new coefficient. 

Here +12 +8 = 20. So our new coefficient is 20

4) Write the new coefficients next to their terms. Here we just have one term, p^2

=20p^2

Other expressions may have many terms.

Can you add p and p^2? They aren't like terms. Can you add x and y? Not like terms. Can you add x^3 and x^3?  Yes! Like terms!

Hope this helps

 

Clint