Collecting Like TermsCollecting Like Terms

Lesson 21Lesson 21

TermsTerms

Literal CoefficientsLiteral Coefficients – are – are variables (letters) that variables (letters) that represent unknown numbers.represent unknown numbers.

Numerical coefficientsNumerical coefficients – are – are numbersnumbers

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

Basically the variable has to be the Basically the variable has to be the same.same.

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

The exponent has to be the same The exponent has to be the same number.number.

Try TheseTry These

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, 3g3g, , -2g-2g, 2g, 2g22, , 5g5g, , ½g½g, , -g-g

Red – Red – 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 therefore we simply add like terms therefore we simply add them like we would if they were them 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

3t3t22 – t – t22 + 2t – 2t+ 2t – 2t (collecting like (collecting like terms)terms)

2t2t22 + 0+ 0 2t2t22

Combining like termsCombining like terms

3ab3ab + 4a+ 4a – 3b– 3b + 4ab+ 4ab – 7a– 7a + 2b+ 2b 3ab + 4ab3ab + 4ab + 4a – 7a+ 4a – 7a – 3b + 2b– 3b + 2b 7ab7ab -3a-3a – b– b

Finished the question because Finished the question because none of the variables are the none of the variables are the same.same.

Class workClass work

Lesson 21 - WorksheetLesson 21 - Worksheet