1. 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 factors know the meaning of the words: factorise expand Next Slide Using PowerPoint to go forward – or to go back –

2. Factorising When there are common factors  CM ppt

3. Factorising When there are common factors Factorising is the opposite to “Removing Brackets”  CM ppt Next Slide 2( 4 + x) = 2×4 = 8 + 2x + 2×x Removing Brackets Factorise = 2( 4 + x) 8 + 2x 2( 4 + x)= 8 + 2x expand (remove brackets) factorise

4.  CM ppt 8x + 40 What number/term goes into both 8x and 40 ? a) 8x + 40 Factorising When there are common factors Factorise the following (put in the brackets) Steps to take: take out the common factor write it outside a bracket inside the brackets, write what is left after the common factor has been taken out : divide each term by the common factor =8( ) 8x ÷ 8 = x write down x in the bracket 40 ÷ 8 = 5 write down + 5 in the bracket x+ 5 What must go inside the brackets? Divide each term by 8. = 8(x + 5) Ans: 8 goes into both so write down 8 and brackets

5.  CM ppt 12x – 9 What number/term goes into both 12x and –9? a) 8x + 40 Factorising When there are common factors Factorise the following (put in the brackets) Steps to take: take out the common factor write it outside a bracket inside the brackets write what is left after the common factor has been taken out : divide each term by the common factor =3( ) 12x ÷ 3 = 4x write down 4x in the bracket - 9 ÷ 3 = 3 write down – 3 in the bracket 4x– 3 What must go inside the brackets? Divide each term by 3. = 8(x + 5) Ans: 3 goes into both so write down 3 and brackets b) 12x – 9 = 3(4x – 3)

6.  CM ppt 6x 2 – 4x What number/term goes into both 6x 2 and –4x ? a) 8x + 40 Factorising When there are common factors Factorise the following (put in the brackets) Steps to take: take out the common factor write it outside a bracket inside the brackets write what is left after the common factor has been taken out : divide each term by the common factor =2x( ) 6x 2 ÷ 2x = 3x write down 3x in the bracket - 4x ÷ 2x = - 2 write down – 2 in the bracket 3x– 2 What must go inside the brackets? Divide each term by 2x. = 8(x + 5) Ans: 2x goes into both so write down 2x and brackets b) 12x – 9 = 3(4x – 3) c) 6x 2 – 4x = 2x(3x – 2)

7.  CM ppt Next Slide 10xy + 5y What number/term goes into both 10xy and 5y ? a) 8x + 40 Factorising When there are common factors Factorise the following (put in the brackets) Steps to take: take out the common factor write it outside a bracket inside the brackets write what is left after the common factor has been taken out : divide each term by the common factor =5y( ) 10xy ÷ 5y = 2x write down 2x in the bracket 5y ÷ 5y = 1 write down + 1 in the bracket 2x+ 1 What must go inside the brackets? Divide each term by 5y. = 8(x + 5) Ans: 5y goes into both so write down 5y and brackets b) 12x – 9 = 3(4x – 3) c) 6x 2 – 4x = 2x(3x – 2) d) 10xy + 5y = 5y(2x + 1) Click here if you need to work through this side again?

8. Time to do some work e.g. 2x + 4 = 2(x + 2) 1) 3(2x + 3) 1) 6x + 9 1) 3(2x + 3) 2) 4(3x + 2) 2) 12x + 8 2) 4(3x + 2) 3) 5(3x – 2) 3) 15x – 10 3) 5(3x – 2) 4) 7x(x + 3) 4) 7x 2 + 21x 4) 7x(x + 3) 5) 2x(7y – 4) 5) 14xy – 8x 5) 2x(7y – 4) Do this is your workbook or on a piece of paper. Write a heading : Exercise 1 : Factorise ONCE YOU HAVE COMPLETED ALL PROBLEMS mark your answers. Next Slide Are you sure that you have written all the answers in your workbook? Only click here if the answer is “YES” Otherwise click backspace.