S k i l l
8 ADDING LIKE TERMS LIKE TERMS have the same literal factor (or factors). 2x + 5y + 4x − 3y The like terms are 2x and 4x, 5y and −3y. What do we do with like terms? We add them: 2x + 5y + 4x − 3y = 6x + 2y That is, we add their coefficients. The coefficient of a literal factor is its numerical factor. Actually, the coefficient of any factor is all the remaining factors. Thus in the term 2xy, the coefficient of x is 2y. In this term, x(x − 1), the coefficient of (x − 1) is x. Problem 1 . 2x + 3y + z a) What number is the coefficient of x? To see the answer, pass your mouse over the colored area. 2 b) What number is the coefficient of y ? 3 c) What number is the coefficient of z ? 1. z = 1· z Problem 2 . 5x − 4y − z a) What number is the coefficient of x ? 5 b) What number is the coefficient of y ? −4. We include the minus sign. Lesson 3. c) What number is the coefficient of z ? −1. −z = (−1)z Problem 3. Add like terms.
i) −3x − 4 + 2x + 6 = −x + 2 j) x − 2 − 4x − 5 = −3x − 7 k) 4x + y − 2x + y = 2x + 2y l) 3x − y − 8x + 2y = −5x + y Problem 4. Add like terms. a) 2a + 3b These are not like terms. The literals are different. b) 2a + 3b + 4a − 5ab
= 6a + 3b − 5ab. Problem 5. Remove parentheses and add like terms.
Problem 6. 5abc + 2cba. Are these like terms?
Yes. The order of factors does not matter. Problem 7. Add like terms.
c) 9xyz + 3yzx + 5zxy = 17xyz d) 3xy − 4xyz + 3x − 8yx + 5yzx − 9x = −5xy + xyz − 6x Problem 8. Add like terms. a) n + (n + 1) = n + n + 1 = 2n + 1 b) n − (n − 1) = n − n + 1 = 1 c) (2n + 1) − (n − 1) = 2n + 1 − n + 1 = n + 2 The subtrahend "Subtract a from b." Is that a − b or b − a ? It is b − a. a is the number being subtracted. It is called the subtrahend. The subtrahend appears to the right of the minus sign. Example. Subtract 2x − 3 from 5x − 4 Solution. 2x − 3 is the subtrahend.
Notice: The signs of the subtrahend change. 2x − 3 changes to −2x + 3. And we add. Problem 9. Subtract 4a − 2b from a + 3b. Change the signs of the subtrahend, and add: a + 3b − 4a + 2b = −3a + 5b Please make a donation to keep TheMathPage online. Copyright © 2001-2007 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |