Lesson 0 of 17
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Show on a big screenYou have x² + 9x + 20. Can you write it as two brackets? By the end of this chapter, yes.
This chapter is Exploring Algebraic Identities. An identity is an equation that is true for all values.
What you will learn
- Cutting down. A square minus a strip.
- One square from another. A subtraction that becomes two brackets at once.
- Three parts. Nine pieces, not three.
- A cube. Four kinds of block inside it.
- The pair. Two numbers with a given sum and a given product.
- A number in front. How to find the pair now.
- Cancelling. What a top and a bottom may share and remove.
- Adding two. A shared bottom, like fractions.
- Your own identity. One disagreement settles a claim.
- Two letters. Squares like (8a + 3b)².
- Two cubes. x³ − y³ and x³ + y³ as brackets.
- A round-number shortcut. Squares in your head.
Need a quick catch-up?
These earlier ideas carry most of the weight.
- Cutting a square into four pieces.
- Two brackets multiplied: four products.
- Taking out a shared factor.
- Matching at every value means two lines are the same.
- Adding fractions with unlike bottoms.