1. Multiplying Polynomials
August 11, 2016

2. Essential question
How do I multiply polynomials?

3. Outline Adding Polynomials Review Subtracting Polynomials Review
Multiplying Polynomials

4. Adding 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

5. Adding Polynomials (Alternate Method)
Add the following polynomials using column form: (4x2 + 3y2) + (-3x2 –xy + 2y2)
(4x2+ 3y2) + (-3x2 - xy + 2y2)
Line up your like terms
4x y2
+ -3x2 - xy + 2y2
X2 -xy + 5y2

6. Subtracting Polynomials
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

7. subtracting Polynomials (Alternate Method)
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
+ 6x2 - 5xy + 7y2
10X2 -7xy + 7y2 + 12

8. Multiplying Polynomials
Multiply a polynomial by a monomial.
Multiply a polynomial by a polynomial.

9. Distributive Property Review
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.

10. Multiplying a polynomial by a monomial
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

11. Multiplying a polynomial by a monomial
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)
Align the terms vertically with the monomial under the polynomial.
2xy – 3x
x___7x
14x2y
– 21x2
Now multiply each term in the polynomial by the monomial.

12. Multiplying a polynomial by another polynomial
We will distribute the first polynomial through the second polynomial.
Multiply: (x + 2)(x – 5)
(x + 2)(x – 5)

13. Multiplying a polynomial by another polynomial
Multiply the First terms. O
Multiply the Outside terms. F
(x + 2)(x – 5)
Multiply the Inside terms.
Multiply the Last terms. I L
After you multiply, collect like terms.
This pattern for multiplying polynomials is called FOIL.

14. Multiplying a polynomial by another polynomial
(x – 6)(2x + 1)
x(2x)
+ x(1)
– (6)2x
– 6(1)
2x2 + x – 12x – 6
2x2 – 11x – 6

15. Examples 2x2(3xy + 7x – 2y) 2x2(3xy) + 2x2(7x) + 2x2(–2y)

16. Examples (x + 4)(x – 3) x(x) + x(–3) + 4(x) + 4(–3) x2 – 3x + 4x – 12

17. Examples (2y – 3x)(y – 2) 2y(y) + 2y(–2) + (–3x)(y) + (–3x)(–2)