Download presentation

Presentation is loading. Please wait.

1
**Revision - Algebra I Binomial Product**

Using Distributive Law to Expand / Remove Brackets. By I Porter

2
**Definitions Binomial Products**

Grouping symbols (…..) can be expanded by using the Disributlive Law. This states that for any real numbers a, b and c: a(b ± c) = ab ± ac Examples: 5(2+3) = 5 x x 3 3(7 - 4) = 3 x x 4 5 x 5 = x 3 = 25 = 25 9 = 9 Binomial Products A binomial expression contains two (2) terms such as : (2 + n), (2x - 5), (3n - 5p) A binomial product is the multiplication of two such binomial expression: (2 + n)(2x - 5), (a - b) (a + b), (2n - 5)(3n + 2), (3p + 4)2. The product of two binomials can be obtained using two approaches: a) the Geometrical Approach - using area diagrams. b) the Algebraic Approach - using the distributive law.

3
**Example: Expand (a + 4) ( a + 2) Algebraic Method**

By the distributive law: Geometrical Method L = last terms I = inside terms (a + 4)(a + 2), can be represented by the area of a rectangle with sides (a + 4) and (a + 2). Area of the rectangle = length x breadth (a + 4)(a + 2) = a a + 2 ) ( + 4 a + 2 ( ) O = outside terms F = first terms = a2 + 2a + 4a + 8 a + 2 + 4 ( ) Area = = a2 + 6a + 8 The area of the large rectangle is equal to the sum of the areas of all the smaller rectangles. F+O+I+L. method of distributive law. a + 4 + 2 FOIL is a mnemonic - a memory jogger - indicating order of multiplication (don’t forget negative signs). F = a x a = a 2 a2 + 4a + 2a + 8 O = a x +2 = +2 a I = +4 x a = +4 a L = +4 x +2 = +8 So, (a + 4)(a + 2) = a2 + 4a + 2a + 8 = a2 + 6a + 8 (a+4)(a+2) = a2 + 4a + 2a + 8 = a2 + 6a + 8 The algebraic method(s) are the preferred.

4
**Distributive Law Method**

x(5x - 2) - 3(5x - 2) Examples: Remove the grouping symbols: 4) (5x - 2)(x - 3) = - - 3 x 5 -3 x 4x = 5x2 -2x -15x + 6 1) -3(4x - 5) = = 5x2 -17x + 6 = -12x + 15 = 3x(3x + 4) + 4(3x + 4) x(x + 4) - 7 (x + 4) 5) (3x + 4)2 = (3x + 4)(3x + 4) 2) (x + 4) (x -7) = = x2 + 4x - 7x - 28 = 9x2 + 12x +12x + 16 = x2 -3x - 28 = 9x2 + 24x + 16 x(2x - 1) + 5(2x - 1) 3) (2x - 1) (x + 5) = Special cases : Difference of two squares. = 2x2 - x + 10x - 5 6) (8 - x) (8 + x) = 8(8 - x) + x(8 - x) = x + 8x - x2 = 2x2 + 9x - 5 = 64 - x2

5
**Exercise: Remove the grouping symbols.**

a) 4y(3 - 2y) = 12y - 8y j) (2x - 1) (x + 4) + (x - 3)2 k) (2x + 3)2 - (x + 4) (x - 3) l) (x - 3)2 + (x - 5)2 = m) (3x - 1)2 - (4x - 1)(x + 5) = n) (5x - 3) (5x + 3) - (4 - x) (4 + x) = = 3x2 + x + 5 b) -8x2 (3 - 2x) = -24x2 + 16x3 c) (x + 9)(3x + 4) = 3x2 + 31x + 36 = 3x2 + 11x + 21 d) (x - 7)(2x - 5) = 2x2 - 19x + 35 e) (3x + 2)(2x + 5) = 6x2 + 19x + 10 = 2x2 - 16x + 34 f) (x + 12)(x - 12) = x g) (3x + 2y)2 = 9x2 + 12xy + 4y2 = 5x2 - 25x + 6 h) (7 - 2xy)2 = xy + 4x2y2 = 26x2 - 25 i) (8x - 3y) (8x + 3y) = 64x2 - 9y2

Similar presentations

Presentation is loading. Please wait....

OK

PSSA Preparation.

PSSA Preparation.

© 2018 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