Collecting Like Terms Lesson 2

Terms Literal Coefficients – are variables (letters) that represent unknown numbers. Literal Coefficients – are variables (letters) that represent unknown numbers. Numerical coefficients – are numbers Numerical coefficients – are numbers Terms – are made up of numerical and literal coefficients. Terms – are made up of numerical and literal coefficients.

Like Terms Terms with identical literal coefficients are like terms. Terms with identical literal coefficients are like terms. EXAMPLE: EXAMPLE: y, 3y, -2y are like terms y, 3y, -2y are like terms x, -2g, 3k are not like terms x, -2g, 3k are not like terms Basically the variable has to be the same. Basically the variable has to be the same.

Like Terms Also the variable needs to be to the same power to be like terms. Also the variable needs to be to the same power to be like terms. Example: Example: y 2, -2y 2, 45y 2 are like terms y 2, -2y 2, 45y 2 are like terms y, -20y 2, 5y 3 are not like terms y, -20y 2, 5y 3 are not like terms The exponent has to be the same number. The exponent has to be the same number.

Try These Which are like terms? Why? Which are like terms? Why? 5b, 3g, -2g, 2g 2, 5g, ½g, -g 5b, 3g, -2g, 2g 2, 5g, ½g, -g

Solution: Which are like terms? Why? Which are like terms? Why? 5b, 3g, -2g, 2g 2, 5g, ½g, -g 5b, 3g, -2g, 2g 2, 5g, ½g, -g Red – like terms. ( they all have the same variable to the same power) Red – like terms. ( they all have the same variable to the same power) White – not like terms. White – not like terms.

Combining Like Terms t + t + t+ t + t t + t + t+ t + t There are five variables which are like terms therefore we simply add them like we would if they were numbers. There are five variables which are like terms therefore we simply add them like we would if they were numbers. t + t + t+ t + t = 5t t + t + t+ t + t = 5t

Combining Like Terms 4t + 3t + t = (4+3+1)t = 8t 4t + 3t + t = (4+3+1)t = 8t 2t – 5t 2 2t – 5t 2 Rearrange the variables so that all like terms are side by side. Rearrange the variables so that all like terms are side by side. 2t 2 – 5t ( notice that the sign in front of the number came with the number) 2t 2 – 5t ( notice that the sign in front of the number came with the number) 2t 2 – 5t = -3t t 2 – 5t = -3t 2 + 8

Combining Like Terms 2t + 3t 2 – 2t –t 2 2t + 3t 2 – 2t –t 2 3t 2 – t 2 + 2t – 2t (collecting like terms) 3t 2 – t 2 + 2t – 2t (collecting like terms) 2t t t 2 2t 2

Combining like terms 3ab + 4a – 3b + 4ab – 7a + 2b 3ab + 4a – 3b + 4ab – 7a + 2b 3ab + 4ab + 4a – 7a – 3b + 2b 3ab + 4ab + 4a – 7a – 3b + 2b 7ab -3a – b 7ab -3a – b The question is FINISHED because none of the variables are the same. The question is FINISHED because none of the variables are the same.

Class work Lesson 21 - Worksheet Lesson 21 - Worksheet