Download 5-3 Add, Subtract, and Multiply Polynomials

5.3B Add, Subtract, and Multiply Polynomials
Name: ______________________
Objective: To add, subtract and multiply polynomials
Algebra 2 Standard 3.0
Adding or Subtracting Polynomials: Add or subtract the coefficients of like terms.
Example 1: Add the polynomials vertically and horizontally.
4 x3  4 x 2  3x  10
a.
b. (3y3 – 2y2 – 7y) + (-4y2 + 2y – 5)
 5 x3  2 x 2  4 x  4


Example 2: Subtract the polynomials vertically and horizontally.
3x3  4 x 2  7 x  12
a.
b. (3y2 – 4y + 7) – (6y2 – 6y – 13)
3
2
 4 x  6 x  9 x  3


You Try: Find the sum or difference using either format.
a. (t2 – 6t + 2) + (5t2 – t – 8)
b. (8d – 3 + 9d3) – (d3 – 13d2 – 4)
Multiplying Two Polynomials: Multiply each term of the first polynomial by each term of the second
polynomial. Use the Distributive Property or Area Models.
Example 3: Multiply the polynomials vertically and horizontally.
a.
 3x

2
 3x  5

 2 x  3
b. (x – 5)(x2 – 2x + 3) *Use an area model.*
Multiplying Three Binomials: multiply the first two binomials and then multiply by the third binomial.
Example 4: (x – 1)(x – 1)(x + 2)
5.3A Notes
You Try: Find the product.
a. ( x + 2)(3x2 – x – 5)
Special Product Patterns
Sum and Difference
b. (y – 5)(y + 2)(y + 6)
Example
(a + b) (a – b)
Square of a Binomial
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
Cube of a Binomial
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
Example 5: Find the product of the binomials.
a. (5y – 3) (5y + 3)
b. (mn – 6)3
You Try: Find the product.
a. (4a + 7)2
b. (2x + 3)3
Example 6: New highway markers are placed every (6x – 6) feet along a stretch of highway. The
total number of markers is represented by x2 – 3x + 1. Write a model for the distance along the
highway where the markers are placed.
5.3A Notes