M4.9.1 For the adult
Expanding two brackets
I know 3(x + 4) = 3x + 12. What do I do when both parts are brackets, like (x + 3)(x + 2)?
What this chapter teaches
To multiply two brackets, every term in the first bracket multiplies every term in the second. A grid keeps the four products in order, and trying a number in both forms catches mistakes.
Three questions to ask
There is no one right wording. Listen for the idea.
- How many products are there when you expand (x + 3)(x + 2), and what are they?
- Why is (x + 3)² not the same as x² + 9?
- How can you check an expansion using a number?
After the chapter, the learner can
- Expand (x + 3)(x − 5)
- Expand (2x + 1)² without losing the middle term
What they copy into their notebook
Multiply every term by every term. Keep each sign with its term. Join the like terms. A squared bracket is the bracket times itself, with four products. Check with a number.