wu #19 1.simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.multiply: (x + 7)(x – 2) 3.multiply: (3x +...
TRANSCRIPT
![Page 1: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/1.jpg)
WU #19
1. Simplify: 4x2 – 2x + 4 + 3x2 + 4x – 1
2. Multiply: (x + 7)(x – 2)
3. Multiply: (3x + 9)(7x – 1)
4. Multiply: (x + 1)(x – 1)
5. Multiply: (2x - 5)(x – 4)
27 2 3x x
2 5 14x x
221 60 9x x 2 1x
22 13 20x x
![Page 2: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/2.jpg)
5.10 Multiplying Binomials: Special Products
• Goal: To multiply the difference of two squares and square a binomial
![Page 3: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/3.jpg)
Foil Multiply: (x + 3)(x – 3)
x2 – 3x + 3x - 9
x2 - 9
![Page 4: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/4.jpg)
Difference of 2 SquaresThe product 0f
(A + B) and (A – B)
is always
The square of the first term minus the square of the
second.(a + b)(a – b) = a2 – b2
![Page 5: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/5.jpg)
Multiply (Mental Math)(3x + 2)(3x – 2) =
9x2
(3x)2
(2)2
-(ALWAYS)
4
![Page 6: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/6.jpg)
Multiply (Mental Math)
(x + 3)(x – 3) =
x2 - 9
![Page 7: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/7.jpg)
Multiply (Mental Math)
(2x + 1)(2x – 1) =
4x2 - 1
![Page 8: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/8.jpg)
Multiply (Mental Math)(2x3 + y)(2x3 – y) =
4x6 -
(2x3) =
(2x3)(2x3) =
2•2•x3•x3 4x6 – y2
![Page 9: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/9.jpg)
Multiply (Mental Math)(4x4 + 3y)(4x4 – 3y)
=16x8 – 9y2
![Page 10: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/10.jpg)
Multiply (Mental Math)(3x + 5)(3x – 5) =
9x2 - 25
![Page 11: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/11.jpg)
Multiply (Mental Math)
1 12 2
5 5x x
2 14
25x
![Page 12: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/12.jpg)
Multiply (Mental Math)
4 43 0.3 3 0.3x x
89 .09x
![Page 13: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/13.jpg)
Multiply: (x + 3)2
x2 + 3x + 3x + 9
Multiplying a binomial by itself is called “squaring the
binomial”
x2 + 6x + 9
(x + 3)(x + 3)
![Page 14: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/14.jpg)
Multiply: (x – 5)2
x2 - 5x - 5x + 25
Multiplying a binomial by itself is called “squaring the
binomial”
x2 - 10x + 25
(x -5)(x-5)
![Page 15: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/15.jpg)
Square of a Binomial
Rules(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
![Page 16: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/16.jpg)
Multiply
(x + 3)2 =
x2 + 6x + 9
Use the rule : (a+b)2 = a2 +2ab +b2
a=x and b = 3, plug it into the formula
x2 +2(x)(3) + 32
![Page 17: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/17.jpg)
Multiply: Mentally Using the Formula
(2t - 5)2 =
4t2 +25- 20t
![Page 18: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/18.jpg)
Multiply: Mentally Using the Formula
(2x + 7)2 =
4x2 + 28x + 49
![Page 19: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/19.jpg)
Multiply: Mentally Using the Formula
(3x – 5y)2 =
9x2 - 30xy + 25y2
![Page 20: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/20.jpg)
Multiply: Mentally Using the Formula
(4x3 – 3x)2 =
16x6 - 24x4 + 9x2
![Page 21: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/21.jpg)
Assignment:
Page 247(2-40) even
![Page 22: WU #19 1.Simplify: 4x 2 – 2x + 4 + 3x 2 + 4x – 1 2.Multiply: (x + 7)(x – 2) 3.Multiply: (3x + 9)(7x – 1) 4.Multiply: (x + 1)(x – 1) 5.Multiply: (2x -](https://reader033.vdocuments.us/reader033/viewer/2022061505/56649d765503460f94a577d5/html5/thumbnails/22.jpg)