1 Multiplication of Brackets - FOIL Saturday, 05 March 2016 © RIVERMEAD Mathematics Department Aim of the lesson:Expand the product of two linear expressions.

Slides:

Advertisements

Similar presentations

Algebra Topic Five – Factorising  CM ppt By the end of this session you should: be able to recognise a common factor factorise expressions with common.

Advertisements

GCSE Mathematics Targeting Grade C Unit 1 Algebra 1.

Identify Linear, Quadratic, and Exponential Functions N Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table.

7.1 – Multiplying Monomials. x · x = x 1 · x 1 =

5.1 Quadratic Function 11/30/12. Graph is a parabola Vocabulary Quadratic Function : a function that is written in the standard form: y = ax 2 + bx +

Fractions, Percents & Decimals

Long Multiplication! Foil Method! Example:

Demonstrate Basic Algebra Skills

Thursday 3 rd March Index laws and notation Objective: To be able to use index notation and apply simple instances of the index laws.

Topic 1Topic 2Topic 3Topic 4Topic

Olympic College Math 94 – Test on Topics 9 to 11

Extending the Distributive Property. You already know the Distributive Property …

4.6 Multiplying Polynomials. Objectives  Multiply two or more monomials  Multiply a polynomial and a monomial  Multiply a binomials by a binomial.

7 th grade Mathematics - 5 Order of Operation 7 th grade Mathematics - 5 Order of Operation.

Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial.

Write the following statement as a mathematical expression using parenthesis and brackets and then evaluate. 51. Multiply 5 by 3.From this product.

Copyright © Cengage Learning. All rights reserved. Polynomials 4.

Whiteboardmaths.com © 2008 All rights reserved

Nat 5 Algebraic Operations Removing Single Brackets - Revision Removing Double Brackets (ax+b)(cx+d) Alternative Method FOIL – (

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

1.(-7) (-2) 2.(3)(-6) 3.(4)(5) 4.(-3) (4t) 5.(2)(-2x) 6.(7y)(3) 7.3(s+5) 8.4(-n+2) 9.4-(t+2) 10.3n+(2-n)

ORDER OF OPERATIONS Making Sense of Math.

Commutative and Associative Properties. Properties are rules in mathematics. You can use math properties to simplify algebraic expressions!

The Distributive Property Chapter 1.6. Review multiplication.

x y Example 1 x y X = 3.

EXAMPLE 3 Multiply polynomials vertically

POLYNOMIALS – Product of Polynomials Binomial times a binomial METHOD 1 : F.O.I.L. FOIL is an acronym for First, Outside, Inside, Last when multiplying.

Expanding Brackets Multiply the contents of the bracket by what is immediately outside it E.g. 3(a+4) 3a3a x a + 3 x 4.

Mathsercise-C Ready? Quadratics Here we go!.

AS Mathematics Algebra – Manipulation of brackets.

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

Order of Operations PEMDAS DON’T STRESS. Numerical Expression : A mathematical phrase that includes numerals and operational symbols. It does not have.

2.8 Inverse of a Sum on Simplifying continued Goal: to simplify expressions involving parenthesis and to simplify with multiple grouping symbols.

Mathsercise-C Expressions 1 Ready? Here we go!. Expressions 1 Simplify the expression…… 1 4p Question 2 Answer + 9q+ 5p– 3q 9p + 6q.

Lesson 2-4 and 2-5 Multiplication and Division of Integers Lesson 2-4 and 2-5.

5.1 Quadratic Function 11/8/13. Graph is a parabola Vocabulary Quadratic Function : a function that is written in the standard form: y = ax 2 + bx + c.

AIM: How do we multiply and divide polynomials?

AIM: How do we simplify, multiply and divide rational expressions?

Exponentials and Logarithms

Mathsercise-C Ready? Expressions 2 Here we go!.

Factoring trinomials ax² + bx +c a = 1

ORDER OF OPERATIONS BEMDAS. 1. Brackets - ( ) or [ ]

Mathematics Algebra and Indices Class 9.

EXPANDING DOUBLE BRACKETS

Collecting Like terms Brackets 2 Brackets

Mathematics Algebra and Indices Class 9.

Maths Unit 14 – Expand, factorise and change the subject of a formula

Area What is the area of these shapes 8 x x2 x x 8x x x 8.

Difference of Two Squares

expanding multiplying a term over a bracket.

Maths Unit 1 - Algebra Order of operations - BIDMAS Algebraic Notation

Factoring Using the Distributive Property

Working with parentheses

Starter Multiply the following 2a x 3b 3s x 4t 4d x 6d 3a x a x b

Factorizing expressions

e.g. 11 & 30 the two numbers are: 5 and 6 because 6 & =11 & 5×6=30

Order of Operations BEDMAS.

Warm Up 10/28/13 -2(x – 7) - (x – 4) (4 – x)(-1) 7a(2a – 3)

EXPANDING DOUBLE BRACKETS

7.5 Multiplying a Polynomial by a Monomial

6.3 ADDING/SUBTRACTING POLYNOMIALS

Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Starter Questions x 2a 3b 4ab 4 7 a b 3a 5b 8a2b 21ab2

Expanding Brackets with Surds and Fractions

A standard way to simplify mathematical expressions and equations.

Maths Unit 15 – Expand, factorise and change the subject of a formula

Multiplying pronumerals

Solving Linear Equations

Presentation transcript:

1 Multiplication of Brackets - FOIL Saturday, 05 March 2016 © RIVERMEAD Mathematics Department Aim of the lesson:Expand the product of two linear expressions. E.g. (x + 1)(x + 2) = x 2 + 3x + 2

2 Reminder: Multiply out the expression 3a(4a + 7) 3a(4a + 7) = 12a² + 21a But what happens when there are 2 brackets (x + 7)(x + 3) Remember the mnemonic F O I L = x² + 3x + 7x + 21 = x² + 10x + 21 First Outside InsideLast

3 Multiply the brackets (x + 6)(x - 4) = x² - 4x + 6x - 24 = x² + 2x - 24 (x - 7)(x + 2) = x² + 2x - 7x - 14 = x² - 5x - 14 (x - 5)² = (x - 5)(x - 5) = x² - 5x + 25 = x² - 10x + 25 (1)(x + 3)(x + 6) (2) (x + 4)(x - 3) (3) (x – 3)(x + 5) (4) (x – 5)(x - 1) (5) (x + 2)² (6) (x – 4)² Left click to see answers x² + 9x + 18 x² + x + 12 x² + 2x – 15 x² – 6x + 5 x² + 4x + 4 x² - 8x + 16

4 To see a dynamic display Then multiplying brackets - Foil

5 Multiply the brackets (2x + 6)(3x - 4) = 6x² - 8x + 18x - 24 = 6x² + 10x - 24 (4x - 7)(3x + 2) = 12x² + 8x - 21x - 14 = 12x² - 13x - 14 (3x - 5)² = (3x - 5)(3x - 5) = 9x² - 15x + 25 = 9x² - 30x + 25 (1)(4x + 3)(5x + 6) (2) (3x + 4)(2x - 3) (3) (5x – 3)(2x + 5) (4) (2x – 5)(2x - 1) (5) (5x + 2)² (6) (3x – 4)² Left click to see answers 20x² + 39x x² - x x² + 9x – 15 4x² – 12x x² + 20x + 4 9x² - 24x + 16

6 Multiply the brackets (5x + 4y)(3x – 4y) = 15x² - 20xy + 12xy - 16y² = 15x² - 8xy - 16y² (5x – 7y)(3x + y) = 15x² + 5xy - 21xy - 7y² = 15x² - 16xy - 7y² (4x – 5y)² = (4x – 5y)(4x – 5y) = 16x² - 20xy + 25y² = 16x² - 40xy + 25y² (1)(4x + y)(5x + 2y) (2) (3x + 2y)(3x – 2y) (3) (5x – 3y)(2x + 3y) (4) (2x – 5y)(3x - y) (5) (x + 2y)² (6) (3x – 7y)² Left click to see answers 20x² + 13xy + 2y² 9x² – 4y² 10x² + 9xy – 9y² 6x² – 17xy + 5y² x² + 4xy + 4y² 9x² - 42xy + 49y²

7 Remember this topic as you will have one of these in your exam. Vocabulary:FOIL Product Expression