Adding Like Terms and Polynomials Like terms are

Adding: “Like Terms” and Polynomials

Like terms are terms that contain the same variables, with corresponding variables having the same power. Example: 3 x 2+4 x+x 2 -2 The like terms in this expression are:

Copy down the following expressions and circle the like terms. 1. 7 x 2+8 x-2 y+8 -6 x 2. 3 x-2 y+4 x 2 -y 3. 6 y+y 2 -3+2 y 2 -4 y 3

Check your answers. 1. 7 x 2+8 x-2 y+8 -6 x 2. 3 x-2 y+4 x 2 -y 3. 6 y+y 2 -3+2 y 2 -4 y 3

To simplify these expressions, you should combine these like terms by adding their coefficients. Rewrite the equations with the like terms combined.

Check your answers. 1. 7 x 2+8 x-2 y+8 -6 x 2. 3 x-2 y+4 x 2 -y 3. 6 y+y 2 -3+2 y 2 -4 y 3

When adding polynomials, you also combine like terms. (2 x 2+3 x-4) + (4 x 2+4 x+8)

You may add these polynomials vertically. Write each polynomial on a separate line, thus keeping them separate without using parentheses. Put like terms beneath each other, even if to do so you must rearrange the terms of a polynomial. 2 x 2+3 x-4 4 x 2+4 x+8

Then combine the like terms. 2 x 2+3 x-4 4 x 2+4 x+8 6 x 2+7 x+4

Or you may do this horizontally by writing the polynomial without the parentheses on one line. 2 x 2+3 x-4+4 x 2+4 x+8

Then combine the like terms. 2 x 2+3 x-4+4 x 2+4 x+8 =6 x 2+7 x+4

Work these on your paper using both methods. 1. (3 x 2+3 x+3) + (4 x 2 -2 x+1) 2. (y 2 -8 y+10) + (3 y 2+8 y+10) 3. (3 a 3+7 a-1) + (3 a 2+3 a-4)