Download presentation

Presentation is loading. Please wait.

Published byMagdalen Roberta Holmes Modified over 4 years ago

1
Multiplication: Special Cases Chapter 4.5

2
Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2

3
( 36x 2 + 42x – 49 – 42x 36x 2 FirstOuter Inner Last – 49 1. Multiply. Use FOIL to multiply. Combine like terms. 6x + 7 )( 6x – 7 )

4
(6x) 2 – (7) 2 36x 2 – 49 ( 1. Multiply. 6x + 7 )( 6x – 7 ) Special Case (a + b)(a – b) = a 2 – b 2 Square the first term. Subtract the square of the second term.

5
(3x) 2 – (5y) 2 9x 2 – 25y 2 ( 2. Multiply. 3x – 5y )( 3x + 5y ) Special Case (a + b)(a – b) = a 2 – b 2 Square the first term. Subtract the square of the second term.

6
(10) 2 – (4a) 2 100 – 16a 2 ( extra. 10 + 4a )( 10 – 4a ) Special Case (a + b)(a – b) = a 2 – b 2 Square the first term. Subtract the square of the second term.

7
(a + b)(a – b) = (a – b)(a + b) =a 2 – b 2 Sum x Difference = Difference of Two Squares

8
Chapter 4.5 Multiplication: Special Cases

9
(a + b) 2 = (a – b) 2 =a 2 – 2ab + b 2 a 2 + 2ab + b 2 Binomial Squared = Perfect Square Trinomial

10
( 16a 2 – 36ab+ 81b 2 – 36ab 16a 2 FirstOuter Inner Last – 72ab+ 81b 2 3a. Multiply. Use FOIL to multiply. Combine like terms. 4a – 9b ) 4a – 9b ) (4a – 9b) ( 2

11
(4a) 2 – 2(4a)(9b) 16a 2 ( 3a. Multiply. 4a – 9b )2)2 Special Case (a – b) 2 = a 2 – 2ab + b 2 Square the first term. Subtract 2 times the first and second terms. Add the square of the second term. + ( - 9b) 2 – 72ab + 81b 2

12
(5x) 2 + 2(5x)(4) 25x 2 ( 3b. Multiply. 5x + 4 )2)2 Special Case (a + b) 2 = a 2 + 2ab + b 2 Square the first term. Add 2 times the first and second terms. Add the square of the second term. + (4) 2 + 40x + 16

13
(3x) 2 – 2(3x)(8) 9x 2 ( extra 3x – 8 )2)2 Special Case (a – b) 2 = a 2 – 2ab + b 2 Square the first term. Subtract 2 times the first and second terms. Add the square of the second term. + ( - 8) 2 – 48x + 64

14
(7x) 2 + 2(7x)(1) 49x 2 ( extra 7x + 1 )2)2 Special Case (a – b) 2 = a 2 – 2ab + b 2 Square the first term. Add 2 times the first and second terms. Add the square of the second term. + (1) 2 + 14x + 1

15
Binomial Squared = Perfect Square Trinomial (a + b) 2 = (a – b) 2 =a 2 – 2ab + b 2 a 2 + 2ab + b 2

16
Chapter 4.5 Multiplication: Special Cases

17
Multiplying Two Trinomials Multiplying Three Binomials

18
4x 3 – 2x 4x 5 + 4x 2 – 8x 3 + 3x 2 – 6x 3 + 12x 4 + x 3 – 2x 4 + 4x 5 – 2x 2 + x x 2 + 3x – 2 + 10x 4 – 13x 3 + 7x 2 – 2x 4. Multiply vertically. (4x 3 – 2x 2 + x)(x 2 + 3x – 2) Multiply each term. Combine.

19
( )( ) 2x 2 – 12 2x 4 – 20x– 8x 2 – 9x– 15x 2 – 6x 3 + 3x 2 + 5x 3 2x 4 + 5x + 3 x2x2 – 3x – 4 – x 3 – 20x 2 – 29x – 12 5. Multiply. Multiply each term. Combine.

20
( – 4 (3x – 2) ( ( 18x 3 – 8x– 12 + 27x 2 ( (2x + 3) 6. Multiply. 9x 2 ) 3x– 2) 3x + 2 ) Sum and difference, rewrite. Special case (a + b)(a – b) = a 2 – b 2. Use FOIL. Can’t combine. (2x + 3) (3x + 2) 2x + 3 )

21
Multiplication: Special Cases Chapter 4.5

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google