ADDING LIKE TERMS
Here is a sum of like terms:
4x² − 5x² + x²
Each term has the same literal factor, x²; only the coefficients are different. The coefficient of x² in the first term is 4. The coefficient in
Here, on the other hand, is a sum of unlike terms:
x² − 2xy + y²
What number is the coefficient of x²?
To see the answer, pass your mouse over the colored area.
What number is the coefficient of xy? −2
What number is the coefficient of y²? 1
Actually, the coefficient of any factor is all the remaining factors. Thus in the term 4ab, the coefficient of a is 4b; the coefficient of 4a is b; and so on. In this term --
Adding like terms
In this sum --
2x + 3y + 4x − 5y
-- the like terms are 2x and 4x, 3y and −5y.
What do we do with like terms? We add, or combine, them:
2x + 3y + 4x − 5y = 6x − 2y.
Problem 1 . 6x − 4y − z
a) What number is the coefficient of x ? 6
b) What number is the coefficient of y ? −4
c) What number is the coefficient of z ? −1. −z = (−1)z. Lesson 6.
Problem 2. What number is the coefficient of x?
Problem 3. How do we add like terms?
Add their coefficients; make that sum the coefficient of the common factor.
Problem 4. 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
m) 4x² − 5x² + x² = 0
Problem 5. Add like terms.
a) 2a + 3b These are not like terms. The literals are different.
b) 2a + 3b + 4a − 5ab
= 6a + 3b − 5ab.
Problem 6. Remove parentheses and add like terms.
Problem 7. 5abc + 2cba. Are these like terms?
Yes. The order of factors does not matter.
Problem 8. Add like terms.
c) 9xyz + 3yzx + 5zxy = 17xyz
d) 3xy − 4xyz + 3x − 8yx + 5yzx − 9x = −5xy + xyz − 6x
Problem 9. Add like terms.
a) 2n + 2 − n = n + 2
b) n − 2 − 3n + 1 = −2n − 1
c) 2n + 4 − 2n − 2 = 2
The rule for subtraction
"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 -- before the word "from."
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.
We can therefore state the following rule for subtraction.
Change the signs of all the terms in the subtrahend.
Problem 10. Subtract 4a − 2b from a + 3b.
Change the signs of the subtrahend, and add:
a + 3b − 4a + 2b = −3a + 5b.
Problem 11. Subtract x² − 5x + 7 from 3x² − 8x − 2.
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Copyright © 2016 Lawrence Spector
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