Factorise by Grouping: The Pair Game
Split the four terms into two teams. Find the common link in each team.
Equation
y = (2*x + 2*4 + 3*x + 3*4) - (2 + 0)*(x + 4)
Graph
Table
| x | y |
|---|---|
| 0 | 12 |
| 1 | 15 |
| 2 | 18 |
| 3 | 21 |
| 4 | 24 |
| 5 | 27 |
What this lesson covers
What you do
You shape the function y = (2*x + 2*c + b*x + b*c) - (2 + k)*(x + c) and watch the graph answer.
Challenges to clear
- Group the pairs: 2(x+c) + b(x+c) = (2+b)(x+c). Slide k to match b — difference 0 at x = 1.
- And at x = 3 — the grouping is exact for every x.
- Group the four terms into two pairs: 5(x + c) + b(x + c). Set b to 4.
- Both pairs share the bracket (x + c), so it factors out once and the other factor is 5 + b. Slide k until the difference is 0 at x = 1.
Check yourself
In the expression ax + ac + bx + bc, why do we group (ax + ac) and (bx + bc) together?
What is the common factor in the first group (ax + ac)?
- To reveal a common binomial factor (x + c) after factoring out a and b. — correct
- To make the expression longer and more complex.
- Because x and c are always the largest numbers.
- To eliminate the variables a and b completely.
- The variable 'a' — correct
- The variable 'x'
- The variable 'c'
- The variable 'b'
Think about it
- 2x + 2c + bx + bc groups as 2(x+c) + b(x+c). What single bracket multiplies (x+c)?