Download Reteach 8-3 ans

Name
Class
8-3
Date
Reteaching
Multiplying Binomials
You can multiply binomials by using the FOIL method. FOIL stands for First,
Outer, Inner, and Last.
Problem
What is the simplified form of (4x 1 3)(2x 1 6)?
Use the FOIL method to simplify the binomial.
Solve
4x ? 2x 5 8x2
Multiply the First terms.
4x ? 6 5 24x
Multiply the Outer terms.
3 ? 2x 5 6x
Multiply the Inner terms.
3 ? 6 5 18
Multiply the Last terms.
8x2 1 24x 1 6x 1 18
Add the products.
8x2 1 30x 1 18
Add the like terms.
Substitute any number for x. Try x 5 2 . If the two sides of the
equation are equal the simplification may be correct.
Check
(4x 1 3)(2x 1 6) 0 8x2 1 30x 1 18
(4 ? 2 1 3)(2 ? 2 1 6) 0 (8 ? 22) 1 (30 ? 2) 1 18
(11)(10) 0 32 1 60 1 18
110 5 110 3
Solution: The simplified form of (4x 1 3)(2x 1 6) is 8x2 1 30x 1 18.
Exercises
Simplify each product.
1. (a 1 6)(a 2 3)
a2
2. (b 2 4)(b 1 5)
b2
1 3a 2 18
4. (2d 1 4)(3d 2 2)
6d2 1 8d 2 8
c2 1 10c 1 21
1 b 2 20
5. (4e 2 5)(3e 1 3)
6. (3f 2 2)(2f 2 4)
12e2 2 3e 2 15
7. (5g 1 3)(g 2 3)
5g2 2 12g 2 9
3. (c 1 3)(c 1 7)
8. (4h 1 4)(2h 1 5)
6f 2 2 16f 1 8
9. (3j 2 5)(4j 2 3)
8h2 1 28h 1 20
12j2 2 29j 1 15
Prentice Hall Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
29
Name
Class
Date
Reteaching (continued)
8-3
Multiplying Binomials
To multiply a trinomial by a binomial, use the same steps as you would to multiply
a 3-digit number by a 2-digit number. Find the partial products for each term of the
binomial and then add the like terms of the partial products.
Problem
What is the simplified form of (2x2 1 3x 2 4)(3x 1 2)?
Solve
Start by arranging the polynomials vertically.
Multiply each part of the trinomial by 2.
2x2 1 3x 2 4
2x2 1 3x 1 2
4x2 1 6x 2 8
2x2 ? 2 5 4x2
3x ? 2 5 6x
24 ? 2 5 28
Multiply each part of the trinomial by 3x.
6x3 1 2x2 1 3x 2 4
6x2 1 4x2 1 3x 1 2
6x3 1 4x2 1 6x 2 8
6x3 1 9x2 2 12x 2 8
2x2 ? 3x 5 6x3
3x ? 3x 5 9x2
24 ? 3x 5 212x
Add the partial products.
6x3 1 4x2 1 6x 2 8
6x3 1 9x2 2 12x 2 8
6x3 1 13x2 2 6x 2 8
Check
Substitute any number for x. Try x 5 2 . If the two sides of the
equation are equal, the simplification may be correct.
(2x2 1 3x 2 4)(3x 1 2) 0 6x3 1 13x2 2 6x 2 8
(8 1 6 2 4)(6 1 2) 0 48 1 52 2 12 2 8
80 5 80 3
Solution: The simplified form of (2x2 1 3x 2 4)(3x 1 2) is 6x3 1 13x2 2 6x 2 8.
Exercises
Simplify each product.
10. (w2 1 3w 2 4)(2w 1 3)
11. (x2 2 8x 1 6)(3x 2 4)
2w3 1 9w2 1 w 2 12
3x3 2 28x2 1 50x 2 24
12. (2y2 1 4y 2 5)(4y 1 2)
8y3 1 20y2 2 12y 2 10
13. (3z2 2 6z 1 4)(4z 1 1)
12z3 2 21z2 1 10z 1 4
Prentice Hall Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
30