Download 3.2A Multiplying Polynomials

3.2A Multiplying Polynomials
Objectives:
A.APR.5: Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and
y for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle.
A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they
are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
For the board: You will be able to multiply polynomials.
You will be able to use binomial expansion to expand binomial expressions that are
raised to positive integer powers.
Bell Work 3.2:
Multiply:
1. x(x3)
4. x(6x2)
2. 3x2(x5)
5. xy(7x2)
3. 2(5x3)
6. 3y2(-3y)
Anticipatory Set:
Open the book to page 158 and read example 1.
Example: Find each product.
a. 4y2(y2 + 3)
4y2(y2) + 4y2(3)
4y4 + 12y2
b. fg(f4 + 2f3g – 3f2g2 + fg3)
fg(f4) + fg(2f3g2) + fg(fg3)
f5g + 2f4g2 – 3f3g3 + f2g4
White Board Activity:
Practice: Find each product.
a. 3cd2(4c2d – 6cd + 14cd2)
12c3d3 – 18c2d3 + 52c2d4
b. x2y(6y3 + y2 – 28y + 30)
6x2y4 + x2y3 – 28x2y2 + 30x2y
Open the book to page 158 – 159 and read example2.
Example: Find each product.
a. (4x – 3)(5x + 2)
4x(5x) + 4x(2) + (-3)(5x) + (-3)(2)
20x2 + 8x – 15x – 6
20x2 – 7x – 6
b. (a – 3)(2 – 5a + a2)
(a – 3)2 – (a – 3)5a + (a – 3)a2
2(a – 3) – 5a(a – 3) + a2(a – 3)
2a – 6 – 5a2 + 15a + a3 – 3a2
a3 – 8a2 + 17a – 6
c. (y2 – 7y + 5)(y2 – y – 3)
y2
-y
-3
4
3
y2
y
-y
- 3y2
3
2
- 7y - 7y
+ 7y
+ 21y
+ 5 + 5y2 - 5y
- 15
y4 – 8y3 + 9x2 + 16x - 15
White Board Activity:
Practice: Find each product.
a. (5x – 2y)(3x + 7y)
5x(3x) + 5x(7y) – 2y(3x) – 2y(7y)
15x2 + 35xy – 6xy – 14y2
15x2 + 29xy – 14y2
b. (3b – 2c)(3b2 – bc – 2c2)
(3b – 2c)3b2 – (3b – 2c)bc – (3b – 2c)2c2
3b2(3b – 2c) – bc(3b – 2c) – 2c2(3b – 2c)
9b3 – 6b2c – 3b2c + 2bc2 – 6bc2 + 4c3
9b3 - 9b2c - 4bc2 + 4c3
2
c. (x – 4x + 1)(x2 + 5x – 2)
x2
+ 5x
-2
4
3
2
x
+ 5x
- 2x2
x
x4 + x3 – 21x2 + 13x - 2
3
- 4x - 4x
- 20x + 8x
+ 1 + x2
+ 5x
-2
Open the book to page 159 and read example 3.
Example: A box is p ft by 3p ft by 4p ft. A larger box was created by adding 2 ft to each dimension.
Write a polynomial V(p) in standard form that can be used to find the volume of the
larger box.
Volume = length ∙ width ∙ height
V(p) = (p + 2)(3p + 2)(4p + 2)
p+2
2
4p
+
2
= (3p + 8p + 4)(4p + 2)
= 12p3 + 32p2 + 16p + 6p2 + 16p + 8
= 12p3 + 38p2 + 32p + 8
3p + 2
White Board Activity:
Practice: A box has a length of x + 3, a width of x + 2, and a height of 2x + 1. Write a polynomial V(x) in
standard form that can be used to find the volume of the box.
Volume = length · width · height
V(x) = (x + 3)(x + 2)(2x + 1) = (x2 + 5x + 6)(2x + 1)
x2
5x
6
3
2
10x
12x
2x 2x
V(x) = 2x3 + 12x2 + 17x + 6
2
1 2x
5x
6
Assessment:
Question student pairs.
Independent Practice:
Text: pgs. 162 – 163 prob. 1 – 9, 18 – 26, 39, 40, 42, 43, 45, 46, 48, 49, 51.
For a Grade:
Text: pgs. 162 – 163 prob. 20, 24, 26, 48.