section 7.8
DESCRIPTION
FOIL. FOIL. Section 7.8 . Multiplying Polynomials. FOIL. FOIL. California Standards. 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques. . (6 3) (y 3 y 5 ). . . - PowerPoint PPT PresentationTRANSCRIPT
Section 7.8 Multiplying Polynomials
FOIL FOIL
FOIL FOIL
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.
California Standards
Multiply.Let’s Try Multiplying Monomials
A. (6y3)(3y5) (6y3)(3y5)
18y8
Group factors with like bases together.
B. (3mn2) (9m2n) (3mn2)(9m2n)
27m3n3
Multiply.
Group factors with like bases together.
Multiply.
(6 3)(y3 y5)
(3 9)(m m2)(n2 n)
3(x + 7) = 3(x) + 3(7) = 3x + 21
-2(-3 + 4y) = -2(-3) + -2(4y) = 6 + -8y
Review of Distributive Property
Multiplying Monomials and Polynomials 4(3x2 + 4x – 8)
4 (3x2 + 4x – 8)
(4)3x2 + (4)4x – (4)8 12x2 + 16x – 32
Distribute 4.
Multiply.
FOIL
FOIL(2x + 1)(x – 5)
(3x - 5)(2x + 7) FOIL
FOIL(3x - 5)(2x + 7)
The box method
12x2
18x
20x
30
12x2 + 38x + 30
The box method
18x2
-12x
3x
-2
18x2 - 9x - 2
The box method
8x2
-4x
-12x
6
8x2 - 16x + 6
The box method
20x3 15x2 -10x
-16x2
20x3 - x2 - 22x + 8
-12x 8
Multiply.Challenge
(x – 5)(x2 + 4x – 6)
(x – 5 )(x2 + 4x – 6)
x(x2 + 4x – 6) – 5(x2 + 4x – 6)
x(x2) + x(4x) + x(–6) – 5(x2) – 5(4x) – 5(–6)
x3 + 4x2 – 6x – 5x2 – 20x + 30
x3 – x2 – 26x + 30
Distribute x and –5.
Distribute x and −5 again.
Simplify.
Combine like terms.
Practice Problems • Fill in the blank.
1. (5a + 2)(6a – 1) = a2 + 7a – 2
2. (2x + 9)(x + 2) = 2x2 + x + 18
3. (x + 3)2 = x2 + + 9
30
13
6x
Match1. (4x + 3)(3x + 2)
2. (2x + 8)(6x + 2)
3. (12x + 3)(x + 1)
4. (6x + 4)(2x + 4)
A. 12x2 + 15x + 3
B. 12x2 + 52x + 16
C. 12x2 + 32x + 16
D. 12x2 + 17x + 6
D
B
A
C
Find Each Product(x + 2)(x + 5)
(2x + 1)(x + 2)
(2y + 1)(3y + 4)
(2x + 3)(x + 5)
(10x + 10)(2x + 2)
(x + 7)2
1.
2.
3.
4.
5.
6.
x2 + 7x + 10
2x2 + 5x + 2
6y2 + 11y + 4
2x2 + 13x + 15
20x2 + 40x + 20
x2 + 14x + 49
Lesson Quiz
Multiply.
1. (6s2t2)(3st)
2. 4xy2(x + y)
3. (x + 2)(x – 8)
4. (2x – 7)(x2 + 3x – 4)
5. 6mn(m2 + 10mn – 2)
6. (2x – 5y)(3x + y)
4x2y2 + 4xy3
18s3t3
x2 – 6x – 162x3 – x2 – 29x + 28
6m3n + 60m2n2 – 12mn
6x2 – 13xy – 5y2