S5 EQU B Path 1

Stage 5 Mathematics Expanding and Factorising

Learning Intentions

For students to begin to expand and factorise binomial products.

Success Criteria

Students will be successful when they can determine missing numbers in various expanding and factorising expressions

Learning Notes

Examples - Given enough information you should be able to find all the other unknown variables

 

4a(3b..)=8a.                 becomes                4a(3b2)=12ab8a

We can see that 4a×3b=12ab. This is the first unknown. Similarly 4a×=8a. This unknown must be -2

 

(x+..)(x+3)=x2+x+15         becomes           (x+5)(x+3)=x2+8x+15

15 is the product of the two back terms. One of these is 3 so the other must be 5. The middle term is the sum of 3 and 5 therefore 8

 

(x+2)(x)=x23x.         becomes           (x+2)(x5)=x23x10

Now, we need to find the middle term first. The sum of the middle terms is -3.  Therefore  2 + ...... = -3.  That is -5.

So the back terms are 2 and -5. The product of these is -10         

 

 

 

 

 

Syllabus Dot Points

selects and applies appropriate algebraic techniques to operate with algebraic fractions, and expands and factorises quadratic expressions

  Lesson Tasks

Introductory Task

1. Expand these basic brackets

.(2x+3)=10x+..

 

2m(+4)=6m2+

 

 

2. Expand these and then simplify if you can

(x3)+15=2x+..

 

10+4(x+..)=..+26

 

 

3. Copy and complete these partially completed expressions

(x+4)(x+.)=x2+.x+20

 

 

(x+10)(x)=x2+4x..

 

 

Open Ended Task

Write three different expressions that when expanded make the statement true

1.      3([..][+[..])+[..]=15x+17

 

2.      ([..][+[..])(x+2)+[..]=x2+6x+10

 

3.      ([..][+[..])(x3)+[..]=2x26x+12

 

Which of these didn't need the final term? Why?

 

Enabling Prompt

Given a and b do not contains fractions or decimals - Which of the following could be an expansion

4(a + b)

8x + 12

14x + 8

16x + 4y

a(3x + b)

12x + 20

18x + 15

9x - 6 

(x + a)(x + b)

x2+5x+5

x2+7x+12

x2+10x+24

 

 

  

Extending Task

Given the expression (x+a)(x+b)=x2+mx20

If a and b are whole numbers find all the different values that they could be?

In each case, what would the value of m be?

Explain how you would determine the value of m?

 

Consolidating Task

Consolidating Task Links to an external site.                  

Other Resources

 

Quiz

Link to quiz