Combining Like Terms Combining Like Terms What are

Combining Like Terms

Combining Like Terms What are “terms”? When are they “like”? How can they be “combined”?

Combining Like Terms What are “terms”? One or more variables being multiplied by a coefficient Examples:

Combining Like Terms What are “terms”? One or more variables being multiplied by a coefficient 5 y variable coefficient 6 s 2 t 3 u variables xyz variables

Combining Like Terms What are “terms”? One or more variables being multiplied by a coefficient 5 y 6 s 2 t 3 u coefficient xyz variables What number is here, even though we don’t see it?

Combining Like Terms When are they “like”? Two terms are “like” if the variables in both terms are exactly the same Same letters Same exponents/powers

Combining Like Terms When are they “like”? Like: 4 cd -7 cd Not like: 3 j 2 k 3 -8 j 3 k 2

Combining Like Terms When are they “like”? Like: 4 cd -7 cd Not like: 3 j 2 k 3 -8 j 3 k 2 Why aren’t these like terms?

Combining Like Terms When are they “like”? Like: 4 cd -7 cd Not like: 3 j 2 k 3 -8 j 3 k 2 Remember: The exponents have to be the same!

Combining Like Terms When are they “like”? Like: 4 cd -7 cd Not like: 3 j 2 k 3 -8 j 3 k 2 The coefficients can be different!

Combining Like Terms Number a piece of paper from 1 to 5.

Combining Like Terms Write whether the pairs of terms are LIKE or NOT LIKE. 1. 5 de 2 f 2. -3 x 4 y 2 3. 2 abc 4. 8 s 3 t 2 u 6 1 5. pq 2 5 def x 4 z 2 -2 abc 4 s 2 t 3 u 6 -6 pq

Combining Like Terms How can they be “combined”? Like terms can be combined through ADDITION and SUBTRACTION.

Combining Like Terms How can they be “combined”? Like terms can be combined through ADDITION and SUBTRACTION. IMPORTANT: Just add or subtract the coefficients. DON’T CHANGE THE VARIABLES!

Combining Like Terms DON’T CHANGE THE VARIABLES! 6 xy + 5 xy = 11 xy -4 p 2 q – p 2 q = -5 p 2 q 2 mn 3 – (-4 mn 3) = 6 mn 3

Combining Like Terms DON’T CHANGE THE VARIABLES! 6 xy + 5 xy = 11 xy -4 p 2 q – 1 p 2 q = -5 p 2 q 2 mn 3 – (-4 mn 3) = 6 mn 3

Combining Like Terms DON’T CHANGE THE VARIABLES! 6 xy + 5 xy = 11 xy -4 p 2 q – p 2 q = -5 p 2 q 2 mn 3 – (-4 mn 3) = 6 mn 3 x + x ≠ 2 x

Combining Like Terms DON’T CHANGE THE VARIABLES! 3 apples + 5 apples = 8 apples NOT 8 applesauce NOT 8 apple pies NOT 8 apple fritters 3 a + 5 a = 8 a NOT 8 a 2

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Term

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression.

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression.

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression. IMPORTANT: Use the sign that comes before the term!

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression. 2 g 2 h

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression. 2 g 2 h

Combining Like Terms You may have an algebraic expression with terms with different combinations of variables. 4 g 2 h + 7 xy 3 – 2 g 2 h – 4 xy 3 Identify like terms and combine them to simplify the expression. 2 g 2 h + 3 xy 3

Combining Like Terms Simplify by combining like terms: -8 uv 3 – 2 a 4 b + 4 u 2 v 3 + 8 a 4 b 7 r 3 s 2 – (-3 de) + 6 de -5 r 3 s 2

Just like you can combine like terms, you can also combine like radicals!

Just like you can combine like terms, you can also combine like radicals! The radicals must be of the same degree. The radicands (the number under the radical) must be the same.

Like Radicals: Not Like Radicals:

Like Radicals: Not Like Radicals (different degree): Not Like Radicals (different radicand):

Like Radicals: Treat like radicals as you would Not Likethe Radicals: like variables and just combine the ”coefficients. ” Not Like Radicals: