Combining like terms

Like terms are terms that contain the exact same variables raised to the same exponents.
**Note x^3 is x raised to power 3

For example, 15yz and 22yz are like terms, but 15yz^2 and 22yz are not.
12 and -6 are like terms, because they are both constant terms .
First group the coefficients of like terms together add the coefficients of
the like terms (or subtract them if they are negative).

Simplify : 11wz + 6w^2 -10wz + wz - 6 - 2w + 3w^2.
6w^2 +3w^2 + 11wz - 10wz + wz - 2w – 6
(note that this expression and the original expression both contain 7 terms)
(6 + 3)w^2 + (11 - 10 + 1)wz - 2w - 6
9w^2 + 2wz - 2w - 6

Practice : Simplify the following expressions
x + 18x^2 + 10 + 7x^2 + 9 + 13x - 14x^2
1 - 15 + 10j + 18j^2 + 12 - 8j^2 + 6j
a - 12a^2 + 11a - 4a + 13a^2 + 6a

Answers:
11x^2 +14x +19
10 j^2 +16j -2
a^2 +13a

Example : combine like terms in the expression 3x + 4y + 6x – 12y - 5x
3x + 4y + 6x – 12y - 5x ( write like terms together)
3x + 6x – 5x + 4y – 12y
9x – 5x - 8y
4x - 8y

Practice: Combine like terms in the following expressions
13z + 11z + 18x - 2y - 3z+ 6y
g + 15k - 4g - 6k + 3k
10p - 5k + 8k + 17p – 4p

Answers:
21z + 4y + 18x
-3g + 12k
23p + 3k