Collecting Like TermsCollecting Like Terms

Lesson 3-2Lesson 3-2

*See smartboard warmup*See smartboard warmup

Terms – Review (do not Terms – Review (do not write this again!)write this again!) Literal CoefficientsLiteral Coefficients – are variables – are variables

(letters) that represent unknown (letters) that represent unknown numbers.numbers.

Numerical coefficientsNumerical coefficients – are numbers – are numbers

TermsTerms – are made up of numerical and – are made up of numerical and literal coefficients.literal coefficients.

Like TermsLike Terms

Terms with Terms with identicalidentical literal literal coefficientscoefficients are are like termslike terms..

EXAMPLE:EXAMPLE: y, 3y, -2y are like termsy, 3y, -2y are like terms x, -2g, 3k are not like termsx, -2g, 3k are not like terms

In other words, like terms must have In other words, like terms must have the same variable.the same variable.

Like TermsLike Terms

Also the variable needs to be to the Also the variable needs to be to the same powersame power to be like terms. to be like terms.

Example:Example: yy22, -2y, -2y22, 45y, 45y22 are like terms are like terms y, -20yy, -20y22, 5y, 5y33 are not like terms are not like terms

In other words, the exponent has to be In other words, the exponent has to be the same number.the same number.

Try ThisTry This

Which are like terms? Why?Which are like terms? Why?

5b, 3g, -2g, 2g5b, 3g, -2g, 2g22, 5g, , 5g, ½g, -g½g, -g

Solution:Solution:

Which are like terms? Why?Which are like terms? Why?

5b, 5b, 3g, -2g3g, -2g, 2g, 2g22, , 5g, 5g, ½g, -g½g, -g

Yellow -Yellow - like terms. ( they all have the like terms. ( they all have the same variable to the same power)same variable to the same power)

White – not like terms.White – not like terms.

Combining Like TermsCombining Like Terms

t + t + t+ t + tt + t + t+ t + t

There are five variables which are There are five variables which are like terms. We simply add them like terms. We simply add them like we would if they were like we would if they were numbers.numbers.

t + t + t+ t + t = t + t + t+ t + t = 5t5t

Combining Like TermsCombining Like Terms

4t + 3t + t = (4+3+1)t = 8t4t + 3t + t = (4+3+1)t = 8t

2t2t22 + 8 – 5t + 8 – 5t22

Rearrange the variables so that all like Rearrange the variables so that all like terms are side by side.terms are side by side.

2t2t22 – 5t – 5t22 + 8+ 8 ( notice that the sign in front ( notice that the sign in front of the number came with the number)of the number came with the number)

2t2t22 – 5t – 5t22 + 8+ 8 = = -3t-3t22 + 8+ 8

Combining Like TermsCombining Like Terms

2t + 3t2t + 3t22 – 2t –t – 2t –t22

= 3t= 3t22 – t – t22 + 2t – 2t+ 2t – 2t

= 2t= 2t22 + 0+ 0

= 2t= 2t22

**Be sure to **Be sure to dodo the addition!! the addition!!

Combining Like termsCombining Like terms

3ab 3ab + 4a+ 4a – 3b– 3b + 4ab + 4ab – 7a– 7a + 2b+ 2b

= 3ab + 4ab = 3ab + 4ab + 4a – 7a+ 4a – 7a – 3b + 2b– 3b + 2b

= 7ab = 7ab -3a-3a – b– b

We have finished the question We have finished the question because none of the variables are because none of the variables are the same.the same.

Class workClass work

Lesson 3-2 – Worksheet (back of Lesson 3-2 – Worksheet (back of handout from yesterday) – please handout from yesterday) – please do on a separate piece of paperdo on a separate piece of paper

You must write the question AND You must write the question AND the answerthe answer