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Combining Like
Terms, Add/Sub
Polynomials and
Distributing
Tammy Wallace
Varina High
Term
A term is a number, variable, or the product of
numbers and variables.
number
5 is a ________________________________
variable
m is a _______________________________
the product of a number
and a variable.
2x² is _________________________________
Constant
A constant is a number add or subtracted to another
term.
5
__________ is the constant in 3x + 4y + 5
2
__________
is the constant in 2 – 3x
Coefficient
A coefficient is the numerical part multiplied in front of
a variable.
4 is the coefficient in front of 4a
______
1 is the coefficient in front of y²
______


______
is the coefficient in front of
5 2
7
Like Term
A like term is a term that has the same variable and
the same exponents.
13k and 22k
5ab and 4ba
3 2 and  2
Simplifying Expressions
To simplify an expression means to add or subtract the
coefficients of all like terms based on the operation in
front of each term.
Simplify 3x + 6x
Because both terms have the same variables which
x
are ________,
they are like terms and can be simplified
equal to
9x
Simplify 8x² + 2x² + 5y + y
Are there any like terms?
Yes
Which ones?
8x² is a like term with 2x²
and
5y is a like term with y
Therefore, once combined, the expression is simplified
to
10x² + 6y
Simplify
1) 5a + 7a
12a
2) 6.1y - 3.2y
2.9y
3) 4x2y + x2y
5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
5) 13a + 8a + 6b
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d
3y
y
7)

4
4
y
Which of the following is the simplified
form of
5x - 4 - 7x + 14 ?
1.
2.
3.
4.
-12x + 10
-2x + 10
2x - 18
12x – 18
Answer Now
Polynomial
A polynomial is a group of two or more terms.
Add the following polynomials:
(9y - 7x + 15a) + (-3y + 8x - 8a)
Group your like terms and simplify
9y - 3y - 7x + 8x + 15a - 8a
6y + x + 7a
Add the following polynomials:
(3a2 + 3ab - b2) + (4ab + 6b2)
Combine your like terms.
3a2 + 3ab + 4ab - b2 + 6b2
2
2
3a + 7ab + 5b
Subtracting Polynomials
Subtracting polynomials is a little different.
When subtracting polynomials, change the
addition and change all other
subtraction sign to _____________
SECOND polynomials to its ______________.
opposite sign
signs in the _________
Subtract the following polynomials:
(9y - 7x + 15a) - (-3y + 8x - 8a)
Rewrite subtraction as adding the
opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Group the like terms.
9y + 3y - 7x - 8x + 15a + 8a
12y - 15x + 23a
5. Subtract the following polynomials:
(7a - 10b) - (3a + 4b)
Rewrite subtraction as adding the
opposite.
(7a - 10b) + (- 3a - 4b)
Group the like terms.
7a - 3a - 10b - 4b
4a - 14b
Find the sum or difference.
(5a – 3b) + (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 3b
Find the sum or difference.
(5a – 3b) – (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 9b
Distributive Property
The Distributive Property is the process of multiplying a
number directly outsides of the parenthesis by
everything inside the parenthesis.
Example
5(x + 7)
5•x+5•7
5x + 35
Distribute
3(m - 4)
3•m-3•4
3m - 12
Distribute
-2(y + 3)
-2 • y + (-2) • 3
-2y + (-6)
-2y - 6
Distribute
2(x² + 4x²y) + 5(3x² - x²y)
2x² + 8x²y + 15x² - 5x²y
2x² + 15x² + 8x²y – 5x²y
10x² +10x²y
Distribute
4(3y² + 4x²y) + (3y² - xy²)
12y² + 16x²y + 3y² - xy²
12y² + 3y² + 16x²y – xy²
15y² + 16x²y – xy²
Distribute
3(3a² + 12) - 2(a² - 1)
9a² + 36 - 2a² + 2
9a² - 2a² + 36 + 2
7a² + 38
Distribute
2(3x² - 6y² + 4x²y) - (3x² + y² - x²y)
6x² - 12y² + 8x²y - 3x² - y² + x²y
6x² - 3x² -12y² - y² + 8x²y + x²y
3x² -13y² + 9x²y