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Chapter 4.5

Chapter 4.5. Multiplication: Special Cases. Difference of Two Squares. Sum x Difference =. (a + b)(a – b) =. a 2 – b 2. ( a – b)(a + b ) =. a 2 – b 2. 1. Multiply. Outer. First. )(. Last. Inner. (. + 7. 6x. ). 6x. – 7. – 49. + 42x. 36 x 2. – 42x. 36 x 2. – 49.

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Chapter 4.5

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  1. Chapter 4.5 Multiplication: Special Cases

  2. Difference of Two Squares Sum x Difference = (a + b)(a – b) = a2– b2 (a – b)(a + b) = a2– b2

  3. 1. Multiply. Outer First )( Last Inner ( + 7 6x ) 6x – 7 – 49 + 42x 36x2 – 42x 36x2 – 49 Use FOIL to multiply. Combine like terms.

  4. 1. Multiply. )( 6x – 7 ( ) 6x + 7 (7)2 – (6x)2 36x2 – 49 Special Case (a + b)(a – b) = a2 – b2 Square the first term. Subtract the square of the second term.

  5. 2. Multiply. 3x + 5y ( ) 3x – 5y )( (5y)2 – (3x)2 9x2– 25y2 Special Case (a + b)(a – b) = a2 – b2 Square the first term. Subtract the square of the second term.

  6. extra. 10 – 4a ( ) 10 + 4a )( (4a)2 – (10)2 100 – 16a2 Special Case (a + b)(a – b) = a2 – b2 Square the first term. Subtract the square of the second term.

  7. Difference of Two Squares Sum x Difference = (a + b)(a – b) = a2– b2 (a – b)(a + b) = a2– b2

  8. Chapter 4.5 Multiplication: Special Cases

  9. Perfect Square Trinomial Binomial Squared = (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2

  10. 3a. Multiply. Outer First Last Inner (4a – 9b) 2 4a ) ( – 9b ( – 9b 4a ) + 81b2 – 36ab 16a2 – 36ab 16a2 – 72ab + 81b2 Use FOIL to multiply. Combine like terms.

  11. 3a. Multiply. ( 4a – 9b )2 – (4a)2 + (-9b)2 2(4a)(9b) + 81b2 16a2 – 72ab Special Case (a – b)2 = a2 – 2ab + b2 Square the first term. Subtract 2 times the first and second terms. Add the square of the second term.

  12. 3b. Multiply. ( 5x + 4 )2 + (5x)2 + (4)2 2(5x)(4) + 16 25x2 + 40x Special Case (a + b)2 = a2 + 2ab + b2 Square the first term. Add 2 times the first and second terms. Add the square of the second term.

  13. extra ( 3x – 8 )2 – (3x)2 + (-8)2 2(3x)(8) + 64 9x2 – 48x Special Case (a – b)2 = a2 – 2ab + b2 Square the first term. Subtract 2 times the first and second terms. Add the square of the second term.

  14. extra ( 7x + 1 )2 + (7x)2 + (1)2 2(7x)(1) + 1 49x2 + 14x Special Case (a – b)2 = a2 – 2ab + b2 Square the first term. Add 2 times the first and second terms. Add the square of the second term.

  15. Perfect Square Trinomial Binomial Squared = (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2

  16. Chapter 4.5 Multiplication: Special Cases

  17. Multiplying Two Trinomials Multiplying Three Binomials

  18. 4. Multiply vertically. (4x3 – 2x2 + x)(x2 + 3x – 2) 4x3 – 2x2 + x + 3x – 2 x2 + 4x2 – 2x – 8x3 + 12x4 – 6x3 + 3x2 + 4x5 – 2x4 + x3 – 13x3 4x5 + 7x2 + 10x4 – 2x Multiply each term. Combine.

  19. 5. Multiply. 2x2 + 5x ( )( ) x2 + 3 – 3x – 4 – 20x + 3x2 – 9x – 12 – 8x2 + 5x3 – 15x2 2x4 – 6x3 – 20x2 2x4 – 29x – x3 – 12 Multiply each term. Combine.

  20. 6. Multiply. (3x – 2) (2x + 3) (3x + 2) ( ( 3x 3x ) – 2 + 2 (2x + 3) ) ) ( ( 9x2 2x + 3 4 ) – – 12 – 8x 18x3 + 27x2 Sum and difference, rewrite. Special case (a + b)(a – b) = a2 – b2. Use FOIL. Can’t combine.

  21. Chapter 4.5 Multiplication: Special Cases

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