Chapter 4.5
21
Multiplication: Special Cases Chapter 4.5
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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. - PowerPoint PPT Presentation
Transcript of Chapter 4.5
Multiplication: Special Cases
Chapter 4.5
Sum x Difference = Difference of Two Squares
(a + b)(a – b) =
(a – b)(a + b) = a2 – b2
a2 – b2
(
36x2 + 42x – 49– 42x
36x2
FirstOuterInnerLast
– 49
1. Multiply.
Use FOIL to multiply. Combine like terms.
6x + 7)(6x – 7)
(6x)2 – (7)2
36x2 – 49
(
1. Multiply.
6x + 7)(6x – 7)
Special Case (a + b)(a – b) = a2 – b2
Square the first term.Subtract the square of the second term.
(3x)2 – (5y)2
9x2 – 25y2
(
2. Multiply.
3x – 5y)(3x + 5y)
Special Case (a + b)(a – b) = a2 – b2
Square the first term.Subtract the square of the second term.
(10)2 – (4a)2
100 – 16a2
(
extra.
10 + 4a)(10 – 4a)
Special Case (a + b)(a – b) = a2 – b2
Square the first term.Subtract the square of the second term.
(a + b)(a – b) =
(a – b)(a + b) = a2 – b2
a2 – b2
Sum x Difference = Difference of Two Squares
Chapter 4.5
Multiplication: Special Cases
(a + b)2 =
(a – b)2 = a2 – 2ab + b2
a2 + 2ab + b2
Binomial Squared = Perfect Square Trinomial
(
16a2 – 36ab + 81b2– 36ab
16a2
FirstOuterInnerLast
– 72ab + 81b2
3a. Multiply.
Use FOIL to multiply. Combine like terms.
4a – 9b) 4a – 9b)
(4a – 9b)
(
2
(4a)2 – 2(4a)(9b)
16a2
(
3a. Multiply.
4a – 9b)2
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.
+ (-9b)2
– 72ab + 81b2
(5x)2 + 2(5x)(4)
25x2
(
3b. Multiply.
5x + 4)2
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.
+ (4)2
+ 40x + 16
(3x)2 – 2(3x)(8)
9x2
(
extra
3x – 8)2
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.
+ (-8)2
– 48x + 64
(7x)2 + 2(7x)(1)
49x2
(
extra
7x + 1)2
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.
+ (1)2
+ 14x + 1
Binomial Squared = Perfect Square Trinomial
(a + b)2 =
(a – b)2 = a2 – 2ab + b2
a2 + 2ab + b2
Chapter 4.5
Multiplication: Special Cases
Multiplying Two Trinomials
Multiplying Three Binomials
4x3
– 2x
4x5
+ 4x2– 8x3
+ 3x2– 6x3+ 12x4
+ x3– 2x4+ 4x5
– 2x2 + xx2 + 3x – 2
+ 10x4 – 13x3 + 7x2 – 2x
4. Multiply vertically.(4x3 – 2x2 + x)(x2 + 3x – 2)
Multiply each term.Combine.
( )( )2x2
– 12
2x4
– 20x– 8x2 – 9x– 15x2– 6x3 + 3x2+ 5x32x4
+ 5x + 3 x2 – 3x – 4
– x3 – 20x2 – 29x – 12
5. Multiply.
Multiply each term.Combine.
( – 4
(3x – 2)(
(
18x3 – 8x – 12+ 27x2
( (2x + 3)
6. Multiply.
9x2 )3x – 2) 3x + 2)
Sum and difference, rewrite.Special case (a + b)(a – b) = a2 – b2.Use FOIL.Can’t combine.
(2x + 3)(3x + 2)
2x + 3)
Multiplication: Special Cases
Chapter 4.5
