Skip to content
Exit presentation

Exploring Algebraic Identities

Start here

You have x² + 9x + 20. Can you write it as two brackets? By the end of this chapter, yes.

A square, minus a strip: (a − b)² = a² − 2ab + b².

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.

Jump to lesson

This track

  1. 0 Start here
  2. 1 A strip cut from a square
  3. 2 One square minus another
  4. 3 A square with three parts
  5. 4 A cube of a sum
  6. 5 Splitting the middle term
  7. 6 Checkpoint: squares, cubes and the first split
  8. 7 A number in front of the square
  9. 8 What may be cancelled
  10. 9 Adding two of them
  11. 10 Proposing one of your own
  12. 11 Checkpoint: coefficients, cancelling and testing
  13. 12 A square with two letters and numbers
  14. 13 Two cubes, one bracket
  15. 14 Squares by a round-number shortcut
  16. 15 The big picture
  17. 16 Track quiz

Other tracks