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

Slides:

Advertisements

Similar presentations

Brackets & Factors OCR Stage 6. What is 3(2 + 4) ? 3 ‘lots’ of ‘2 + 4’= 3 ‘lots’ of 6= x 6 12 = 18.

Advertisements

Expanding and Factorising. Expanding Can’tcannot What is ‘expanding’?

QUADRATICS EQUATIONS/EXPRESSIONS CONTAINING x2 TERMS.

Factorising polynomials This PowerPoint presentation demonstrates two methods of factorising a polynomial when you know one factor (perhaps by using the.

Grade 10 Mathematics Products and rules.

Factorising Cubics (Example 1) Factorise x 3 + 7x 2 + 7x  15 given that (x + 3) is a factor x 3 + 7x 2 + 7x  15 = (x + 3)(x 2 + ax  5) x 3 + 7x 2 +

An alternative to the trial and improvement method Factorising Difficult Quadratics.

Foil Method F=First O=Outside I=Inside L=Last. (x+7)(x+4) First= multiply the first terms in each binomial.(highlighted in blue) x 2.

Binomial Expansions Reflection. What is a binomial? A binomial is a mathematical expression of two unlike terms with coefficients and which is raised.

Demonstrate Basic Algebra Skills

We Are Learning To We Are Learning To

Multiplying Polynomials In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.

Brackets Factors and Equations

Whiteboardmaths.com © 2008 All rights reserved

Quadratic Equations Learning Outcomes  Factorise by use of difference of two squares  Factorise quadratic expressions  Solve quadratic equations by.

Chapter 5.2 Solving Quadratic Equations by Factoring.

Quadratic Factorising If you can long multiply you can factorise!

Solving a quadratic by factorisation 6x 2 + 7x – 3 = 0 ac = -18 b = 7 Factors are: , , +2 -9, , , Correct pair adding to.

Multiplying Polynomials Use the distributive property, and remember your properties for exponents. 5x (4x 2 + 3x) = 20x x 2 Section 10.2.

GSE Algebra I EQ: How do you multiply polynomials? Standard: M.ALGI.4.14: Polynomials: Multiply.

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

Expanding Brackets Objectives: D GradeMultiply out expressions with brackets such as: 3(x + 2) or 5(x - 2) Factorise expressions such as 6a + 8 and x 2.

Mathsercise-C Ready? Quadratics Here we go!.

Algebra Expanding Brackets. Algebra So far we have looked at simplifying expressions like 3x + 2y + 2x + 4y collecting the like terms to make 5x + 6y.

Algebra Factorising into single brackets Grade 2.

Introduction This chapter focuses on basic manipulation of Algebra It also goes over rules of Surds and Indices It is essential that you understand this.

LAWS OF EXPONENTS LAW 1: (base)power x (same base)another power

11/06/ Factorizing Quadratic Equations. 11/06/ x 2 ± bx ± c x 2 ± bx ± c If this is positive, both signs are the same. The numbers ADD to.

Factoring Day 1 I can factor a quadratic expression. x 2 + 3x + 2 Rewrite as (x + 1)(x + 2)

Expanding Brackets and Simplifying

GCSE: Algebraic Fractions

Factor a quadratic expression

Quadratic Equations.

Solving quadratic equations

Mathematics Algebra and Indices Class 9.

Literacy Research Memory Skill Practice Stretch!

Algebraic Expressions

Factoring Quadratic Equations

Quadratic expressions with 2 terms

Literacy Research Memory Skill Practice Stretch

Mathematics Algebra and Indices Class 9.

Fraction in Simplest form

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

Factors – Learning Outcomes

Expanding (brackets).

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

expanding multiplying a term over a bracket.

Next week is revision week

fACTORISING quadratics

Factoring Quadratic Equations

Factorising quadratics

Unit 23 Algebraic Manipulation

Two-step with common factor

Factors A factor is a number or letter that will divide exactly into another number or expression without leaving a remainder Examples (a) Factors of 12…

F=First O=Outside I=Inside L=Last

Factorising: Quadratics with Single Bracket

Find 2 numbers that … Multiply together to make the top number in the wall and sum to make the bottom number 20 9.

Algebra – Brackets 2 L.O. All pupils can expand linear expressions

Expand Brackets Low C C B

6.3 ADDING/SUBTRACTING POLYNOMIALS

Factorisation. Single Brackets.

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

Factoring Polynomials

1) Expand Brackets 2) Factorise

Introduction to factorisation

Discuss: What are the 4 different ways we can factorise an expression?

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

Presentation transcript:

What 2 numbers add to give the first number and multiply to give the second number … e.g. 11 & 30 the two numbers are: 5 and 6 because 6 & 8. 5+6=11 & 5×6=30 9 & 14. 9 & 18. 7 & 10. 10 & 21. 11 & 10 11 & 28 13 & 40 13 & 36 11 & 24 1 & -6 1 & -12 4 & -21 7 & -18 2 & -24 1 & -30 2 & -35 6 & -27 -1 & -20 -4 & -12 -4 & -21 -5 & -50 -8 & -9 -4 & -45 -5 & -24 -4 & -5

Factorising (One Bracket) 7x+7y= 8x+12= 3x+x2= 12x2+6x= p2q3-pq2= 18xy2-12x2y2=

Expanding (x+3)(x-6) FOIL is a mnemonic used for expanding quadratic expressions (2 brackets) F=First O=Outer I=Inner L=Last (first ______)(first_____) (x+3)(x-6) (outer______)(_____outer) (x+3)(x-6) ( _____ inner)(inner _____) (x+3)(x-6) ( ______last)( ______ last) (x+3)(x-6)

Factorising (2 Brackets) Factorising is the reverse of Expanding. You are finding the factors. (x+4)(x-2) = x2+2x-8 What two numbers multiply to give -8 and add to give +2? x2+8x+15 what two numbers multiply to give and add to give +3 and +5 So x2+8x+15 factorised is (x+3)(x+5) or (x+5)(x+3) You do: Factorise a) x2+9x+14 (x+4)(x-2)= +4 and -2 Factors of 15 are 1×15 & 3×5

One positive factor & one Negative factor… x2 + 2x – 24 Two numbers that multiply to give -24 and add to give +2. Write down all the factors of 24: -1×24, -2×12, −3×8, -4×6, 1×-24, 2×-12, 3×-8, 4×-6. Which pair add to give +2? These are our factors. x2 + 2x – 24 = (x-4)(x+6) Your Turn: x2 + 3x - 40