# finding expression and combining like terms

• Feb 21st 2007, 03:00 PM
Patience
finding expression and combining like terms
1. A triangle has sides 3x + 7, 4x , and 5x + 6. Find the expression
that represents its perimeter.

Combining like terms

2. 7(4w-3)-25w
• Feb 21st 2007, 05:09 PM
Aryth
Quote:

Originally Posted by Patience
1. A triangle has sides 3x + 7, 4x , and 5x + 6. Find the expression
that represents its perimeter.

Combining like terms

2. 7(4w-3)-25w

1. To find the perimeter of a triangle we use this equation:

P = a + b + c

Where a, b, and c are the sides of the triangle.

So we just plug in the sides:

P = (3x + 7) + (4x) + (5x + 6)

Now we take out the parentheses:

P = 3x + 7 + 4x + 5x + 6

To combine like terms we look at each number and if they have certain things in common, we can add them.

For the variables, any number that has a variable next to it can be added if the variables share the same power and the same variable, for example:

2x + 5x = 7x

They both share x^1 so they can be added, on the other hand:

2x + 5x^2 = 2x + 5x^2

They cannot be added because x and x^2 are not the same.

Let's go back to the perimeter, we are going to go ahead and separate like terms:

P = (3x + 4x + 5x) + (7 + 6)

P = 12x + 13

Because,

3x + 4x + 5x = 12x

Now for number 2:

7(4w-3)-25w

The like terms in here are 4w and -25w and 7 and -3. But the 7 is being distributed among th 4w-3 so let's look at it separately:

7(4w - 3) = 7(4w) - 7(3) = 28w - 21

The thing here is you can multiply ANY two terms regardless of if they are like terms, thus we can multiply 7 by 4w.

Let's plug that back into the original problem:

28w - 21 - 25w = (28w - 25w) - 21 = 3w -21

I hope you understand it now. ^_^