Subtract the first term from the second term .1 2xy
Answers
Answered by
2
WHEN NUMBERS ARE ADDED OR SUBTRACTED, we call them terms. (Lesson 1.) Like terms look exactly alike, except perhaps for a numerical factor, which is called the coefficient of the term.
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
the second term is −5. We include the minus sign. See Naming terms in Lesson 3. And in the last term, the coefficient of x² is understood to be 1. For, x² = 1x². (Lesson 6.)
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.
To cover the answer again, click "Refresh" ("Reload").
1
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 --
x(x − 1) -- the coefficient of (x − 1) is x.
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.
That is, we add (Lesson 3) their coefficients. The order of the terms does not matter.
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?
a) x
2. 1
2. Compare Lesson 5, Problem 7b. b) 3x
4. 3
4. 3x
4= 3
4· x Lesson 4.
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.
a) 6x + 2x= 8x b) 6x − 2x= 4x c) 5x + x= 6x d) 5x − x= 4x e) −4x + 5x= x f) 4x − 5x= −x It is the style in algebra not to write the coefficients 1 or −1. g) −5x − 3x= −8x h) −x − x= −2x
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.
Terms that you cannot combine, simply rewrite.
Problem 6. Remove parentheses and add like terms.
a) (2a − 3b + c) + (5a − 6b + c) = 2a − 3b + c + 5a − 6b + c = 7a − 9b + 2c b) (a + 2b + 4c − 3d) − (3a − 8b − 2c + d) = a + 2b + 4c − 3d −3a + 8b + 2c − d = −2a + 10b + 6c − 4d c) (4x − 3y) + (3y − 5x) + (5z − 4x) = 4x − 3y + 3y − 5x + 5z − 4x = −5x + 5z d) (5xy − 3x + 2y − 1) − (2xy − 7x − 8y + 6) = 5xy − 3x + 2y − 1 −2xy + 7x + 8y − 6 = 3xy + 4x + 10y − 7 e) (x − y) − (y + xy − x) − (2x − 4xy − 2y) = x − y −y − xy + x − 2x + 4xy + 2y = 3xy f) (4x² − 7x − 3) − (x² − 4x + 1) = 4x² − 7x − 3 − x² + 4x − 1 = 3x² − 3x − 4 g) (6x3 + 4x² − 2x − 6) − (2x3 − 8x² + x − 2) = 6x3 + 4x² − 2x − 6 − 2x3 + 8x² − x + 2 = 4x3 + 12x² − 3x − 4 h) (x² + x + 1) + (2x² + 2x + 2) − (x² − x − 1) = x² + x + 1 + 2x² + 2x + 2 − x² + x + 1 = 2x² + 4x + 4
Problem 7. 5abc + 2cba. Are these like terms?
Yes. The order of factors does not matter.
Upon adding those like terms, we get 7abc.
When writing the final answer, it is conventional to preserve the alphabetical order.
Problem 8. Add like terms.
a) 4xy − 9yx = −5xy b) 8x − 5xy − 4x + 4yx = 4x −xy
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.
(5x − 4) − (2x − 3)=5x − 4 − 2x + 3 =3x − 1.
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.
Then add the like terms.
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.
3x² − 8x − 2 − x² + 5x − 7 = 2x² − 3x − 9.
Next Lesson: Linear equations
Table of Contents | Home
Please make a donation to keep TheMathPage online.
Even $1 will help.
Copyright © 2018 Lawrence Spector
Questions or comments?
E-mail: [email protected]
Private tutoring available.
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
the second term is −5. We include the minus sign. See Naming terms in Lesson 3. And in the last term, the coefficient of x² is understood to be 1. For, x² = 1x². (Lesson 6.)
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.
To cover the answer again, click "Refresh" ("Reload").
1
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 --
x(x − 1) -- the coefficient of (x − 1) is x.
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.
That is, we add (Lesson 3) their coefficients. The order of the terms does not matter.
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?
a) x
2. 1
2. Compare Lesson 5, Problem 7b. b) 3x
4. 3
4. 3x
4= 3
4· x Lesson 4.
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.
a) 6x + 2x= 8x b) 6x − 2x= 4x c) 5x + x= 6x d) 5x − x= 4x e) −4x + 5x= x f) 4x − 5x= −x It is the style in algebra not to write the coefficients 1 or −1. g) −5x − 3x= −8x h) −x − x= −2x
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.
Terms that you cannot combine, simply rewrite.
Problem 6. Remove parentheses and add like terms.
a) (2a − 3b + c) + (5a − 6b + c) = 2a − 3b + c + 5a − 6b + c = 7a − 9b + 2c b) (a + 2b + 4c − 3d) − (3a − 8b − 2c + d) = a + 2b + 4c − 3d −3a + 8b + 2c − d = −2a + 10b + 6c − 4d c) (4x − 3y) + (3y − 5x) + (5z − 4x) = 4x − 3y + 3y − 5x + 5z − 4x = −5x + 5z d) (5xy − 3x + 2y − 1) − (2xy − 7x − 8y + 6) = 5xy − 3x + 2y − 1 −2xy + 7x + 8y − 6 = 3xy + 4x + 10y − 7 e) (x − y) − (y + xy − x) − (2x − 4xy − 2y) = x − y −y − xy + x − 2x + 4xy + 2y = 3xy f) (4x² − 7x − 3) − (x² − 4x + 1) = 4x² − 7x − 3 − x² + 4x − 1 = 3x² − 3x − 4 g) (6x3 + 4x² − 2x − 6) − (2x3 − 8x² + x − 2) = 6x3 + 4x² − 2x − 6 − 2x3 + 8x² − x + 2 = 4x3 + 12x² − 3x − 4 h) (x² + x + 1) + (2x² + 2x + 2) − (x² − x − 1) = x² + x + 1 + 2x² + 2x + 2 − x² + x + 1 = 2x² + 4x + 4
Problem 7. 5abc + 2cba. Are these like terms?
Yes. The order of factors does not matter.
Upon adding those like terms, we get 7abc.
When writing the final answer, it is conventional to preserve the alphabetical order.
Problem 8. Add like terms.
a) 4xy − 9yx = −5xy b) 8x − 5xy − 4x + 4yx = 4x −xy
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.
(5x − 4) − (2x − 3)=5x − 4 − 2x + 3 =3x − 1.
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.
Then add the like terms.
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.
3x² − 8x − 2 − x² + 5x − 7 = 2x² − 3x − 9.
Next Lesson: Linear equations
Table of Contents | Home
Please make a donation to keep TheMathPage online.
Even $1 will help.
Copyright © 2018 Lawrence Spector
Questions or comments?
E-mail: [email protected]
Private tutoring available.
Answered by
3
Answer:
Step-by-step explana8x,-9x
Similar questions