Download 8.5 using FOIL ink.notebook

8.5 using FOIL ink.notebook
January 11, 2017
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8.5 FOIL
Multiply
Polynomial by
Polynomial
Lesson Objectives
Standards
Lesson Notes
Lesson Objectives
Standards
Lesson Notes
8.5 ­ Using Foil
A.APR.1 I will simplify polynomial expressions by multiplying a polynomial by a polynomial Press the tabs to view details.
Press the tabs to view details.
1
8.5 using FOIL ink.notebook
Lesson Objectives
Standards
January 11, 2017
Lesson Notes
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.
FOIL
Outer
First
(x + y) (x + y)
Inner
Last
Press the tabs to view details.
x2 + xy + xy + y2 = x2 + 2xy + y2
Multiplying Polynomial by Polynomial
a) (x + 4)(x - 9)
Distribute EACH term of the first polynomial
to EACH term of the second polynomial
Multiply the big numbers and
add the little exponents
b) (3x - 7)2
(little 2 means write it twice)
Find each product.
1. (x + 8)(5x ­ 6) = (x + 3)(x - 7)
_____ _____ ______ _____ = ___________________________
2. (x ­ 2)(x + 3)
(x)(x) +
(x)(-7)
+ (3)(x) +
3. (5x ­ 3)(2x + 8)
(3)(-7)
4. (w ­ 6)(w + 6) 5. (x ­ 4)2
x - 7x + 3x - 21
2
x2 - 4x - 21
2
8.5 using FOIL ink.notebook
January 11, 2017
a) (x + 4)(x - 9)
b) (3x - 7)2
(little 2 means write it twice)
Find each product.
1. (x + 8)(5x ­ 6) = Find each product.
4. (w ­ 6)(w + 6) 5. (x ­ 4)2
_____ _____ ______ _____ = ___________________________
2. (x ­ 2)(x + 3)
3. (5x ­ 3)(2x + 8)
3
8.5 using FOIL ink.notebook
January 11, 2017
Find each product.
6. (x + 2y)2
7. (x + 3y)(x – y) 8. (x + 5)(x2 ­ 4x + 2)
9. (5x – 8)(x2 – 3x + 4) 10. (x2 + x + 5)(x2 – 5x + 2)
Find each product.
6. (x + 2y)2
7. (x + 3y)(x – y) Find each product.
8. (x + 5)(x2 ­ 4x + 2)
4
8.5 using FOIL ink.notebook
January 11, 2017
Find each product.
9. (5x – 8)(x2 – 3x + 4) Find each product.
10. (x2 + x + 5)(x2 – 5x + 2)
5
8.5 using FOIL ink.notebook
On Your
Whiteboards
January 11, 2017
On the
Worksheet
Give the missing term.
1. (y + 3)(y + 2) = y2 + 5y + ____
Homework
2. (x – 4)(x + 7) = x2 + 3x + ____
3. (x + 8)(x – 9) = x2 + ____ – 72 6
8.5 using FOIL ink.notebook
Give the missing term.
January 11, 2017
Find each product.
4. (n – 3)(n + 7) = n2 + ____ – 21
7. (2x + 1)(3x – 1) _____ _____ ______ _____ = ___________________________
5. (3y + 2)(y – 4) = ___ – 10y – 8
8. (9x ­ 1)(9x + 1) 6. (4x + 7)(5x – 1) = ____ + 31x – 7
9. (6 + c)(6 + c) 10. (7x – 1)(7x – 1)
11. (7 ­ 8d)(7 + 8d) 12. (9x – 2)(9x + 2) 7
8.5 using FOIL ink.notebook
13. (2y + 1)2 17. (2x – 3)(x2 – 4x + 9) 14. (3x – 4)2 January 11, 2017
15. (7x – 2)2 16. (4x – 3y)2
18. (c + 1)(c2 – 2c + 1) 8
8.5 using FOIL ink.notebook
January 11, 2017
19. (8n – 2)(2n2 + n – 3) 20. (n – 2)(n2 + 5n – 6) 21. (3x + 4)( x2 + 3x – 4)
22. (x2 + 4x + 3)(4x2 – x + 3) 9
8.5 using FOIL ink.notebook
Add or Subtract.
January 11, 2017
25. (x + 3) + (5x ­ 10) 23. (4x + 3) + (6x ­ 2) 24. (6x + 1) ­ (8x + 7) 27. (5y + 2) + (4y – 12) 28. (9x – 6) – (7x + 1) 26. (3x + 2) ­ (5x + 4) 29. (4x + 11) – (8x + 3) 30. (12x + 3) – (6x – 2) 10
8.5 using FOIL ink.notebook
January 11, 2017
Express the area of each figure as a polynomial in simplest form.
31. 2(7x + 4) – 3(8x + 1) 32.
2x + 3
33.
2x + 3
2x + 3
36.
35.
4x + 2
6x + 7
6x + 7
6x + 7
6x + 7
5n ­ 3
37.
7n ­ 1
n + 3
n + 3
7n ­ 1
n + 6
n + 6
2x + 3
34.
5n ­ 3
8x + 6
2x ­ 5
3x ­ 2
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8.5 using FOIL ink.notebook
January 11, 2017
Answers:
1) 6 3) –1x 5) 3y2 7) 6x2 – 2x + 3x – 1 = 6x2 + x – 1 9) c2 + 12c + 36 11) –64d2 + 49 13) 4y2 + 4y + 1 15) 49x2 – 28x + 4 17) 2x3 – 11x2 + 30x – 27
19) 16n3 + 4n2 – 26n + 6 21) 3x3 + 13x2 – 16 23) 10x + 1 25) 6x – 7 27) 9y – 10 29) –4x + 8 31) –10x + 5 33) 5n2 + 27n – 18 35) 36x2 + 84x + 49 37) 8x2 – 14x – 15 12