Algebraic Manipulation Worksheets With Answers - Craven Community College Page 6
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29Adding and Subtracting Polynomials
Simplifying polynomials is very similar to simplifying algebraic expressions. First remove all grouping
symbols; then simplify each term and finally combine all like terms. Adding polynomials means adding
the like terms together. To subtract polynomials, change the signs of the second polynomial and then add
the polynomials.
3
2
Example 1:
Add
(3X
– 7X + 2) + (7X
+ 2X – 7)
3
2
(3X
+ 7X
+ (-7X + 2X) + (2 – 7)
Use the properties to group
like terms together
3
2
3X
+ 7X
– 5X – 5
2
2
Example 2:
Subtract
(5X
+ 3X – 6) – (3X
– 5X + 2)
2
2
(5X
+ 3X – 6) + (-3X
+ 5X – 2)
Change the signs and add
2
2
(5X
– 3X
) + (3X + 5X) + (-6 – 2) Group like terms
2
2X
+ 8X – 8
Multiply Polynomials
To multiply a monomial times a polynomial, use the distributive property.
2
2
Example 1:
-3X
(4X
– 5X +11)
2
2
2
2
-3X
(4X
) – 3X
(-5X) – 3X
(11)
Use the distributive property
4
3
2
-12X
+ 15X
– 33X
Simplify each term
To multiply a polynomial times another polynomial, use the distributive property to multiply each term of
the first polynomial by each term of the second polynomial.
2
Example 2:
(X-2)(X
+ 3X – 4)
2
X(X
+ 3X – 4) – 2(X2 + 3X – 4)
Distributive property
2
2
X(X
) + X(3X) + X(-4) – 2(X
) – 2(3X) – 2(-4)
Distributive property again
3
2
2
X
+ 3X
– 4X – 2X
– 6X + 8
Simplify each term
3
2
2
X
+ (3X
– 2X
) + (-4X – 6X) + 8
Group like terms
3
2
X
+ X
– 10X + 8
Add like terms
To multiply two binomials together use the shortcut called the FOIL method.
2
Example 3:
(2X + 4)(X – 7) = 2X
– 14X + 4X – 28
First terms
(2X)(X)
Outer terms
(2X)(-7)
F
O
I
L
Inner terms
(4)(X)
Last terms
(4)(-7)
2
2X
– 10X – 28
Add like terms
6
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