Download Adding, Subtracting, and Dividing Polynomials

August 11, 2016
How do I multiply polynomials?
Adding Polynomials Review
Subtracting Polynomials Review
Multiplying Polynomials
Add the following polynomials:
(9x2 - 7x + 15) + (-3x2 + 9x - 8)
Step 1: Group all like terms together
(9x2-3x2) +(-7x+9x) +(15-8)
6x2 + 2x +7
Step 2: Make sure the expression is standard form
Add the following polynomials using column form:
(4x2 + 3y2) + (-3x2 –xy + 2y2)
(4x2+ 3y2) + (-3x2 - xy + 2y2)
Line up your like terms
4x2
+ 3y2
+ -3x2 - xy + 2y2
X2 -xy + 5y2
Subtract the following polynomials:
(9x2 - 7x + 15x3) - (-3x2 + 8x - 8x3)
Step 1: Rewrite subtraction as adding the
opposite.
(9x2 - 7x + 15x3) + (+ 3x2 - 8x + 8x3)
Step 2: Group the like terms.
(9x2 + 3x2)+ (- 7x - 8x) + (15x3 + 8x3)
12x2-15x+23x3  23x3+12x2-15x
Add the following polynomials using column form:
(4x2 – 2xy + 12) - (-6x2 +5xy - 7y2)
(4x2 - 2xy + 12) + (6x2 - 5xy + 7y2)
Line up your like terms
4x2 - 2xy
+ 12
+ 6x2 - 5xy + 7y2
10X2 -7xy + 7y2 + 12
Multiply a polynomial by a monomial.
Multiply a polynomial by a polynomial.
Consider the following expression: 3 (x+6) This
expression is the sum of x and 6 multiplied by 3.
3(x + 6)
(3 *x) +(3 *6)
3x + 18
To simplify this expression we can distribute the
multiplication by 3 to each number in the sum.
Multiply: 3xy(2x + y)
This problem is just like the review problems except for
a few more variables.
To multiply we need to distribute the 3xy over the
addition.
3xy(2x + y) = (3xy * 2x) + (3xy * y) = 6x2y + 3xy2
 We can also multiply a polynomial and a monomial using a vertical
format in the same way we would multiply two numbers.
 Multiply: 7x(2xy – 3x)
2xy – 3x
x___7x
14x2y – 21x2
Align the terms vertically with the
monomial under the polynomial.
Now multiply each term in the
polynomial by the monomial.
We will distribute the first polynomial through
the second polynomial.
Multiply: (x + 2)(x – 5)
(x + 2)(x – 5)
O
F
(x + 2)(x – 5)
I
Multiply the First terms.
Multiply the Outside terms.
Multiply the Inside terms.
Multiply the Last terms.
L
After you multiply, collect like terms.
This pattern for multiplying polynomials is called FOIL.
(x – 6)(2x + 1)
x(2x)+ x(1) – (6)2x – 6(1)
2x2 + x – 12x – 6
2x2 – 11x – 6
2x2(3xy + 7x – 2y)
2x2(3xy) + 2x2(7x) + 2x2(–2y)
6x3y + 14x3 – 4x2y
(x + 4)(x – 3)
x(x) + x(–3) + 4(x) + 4(–3)
x2 – 3x + 4x – 12
x2 + x – 12
(2y – 3x)(y – 2)
2y(y) + 2y(–2) + (–3x)(y) + (–3x)(–2)
2y2 – 4y – 3xy + 6x