Mathematics Class 9
Exploring Algebraic Identities
Expand and factor squares, cubes and quadratics, and use identities to compute.
17 lessons · ~135 min total
Track progress — 0 of 17 lessons read 0%
Lessons in this topic
- 0 Start here A roadmap for identities: squares, cubes, splitting the middle term, cancelling and adding fractions. · 4 min You are here
- 1 A strip cut from a square Cutting a strip off two edges of a square leaves (a − b)² = a² − 2ab + b². · 8 min
- 2 One square minus another a² − b² = (a − b)(a + b). The gap times the total. · 8 min
- 3 A square with three parts (a + b + c)² has nine pieces: three squares and six matching rectangles. · 8 min
- 4 A cube of a sum (a + b)³ = a³ + 3a²b + 3ab² + b³. Four kinds of block fill the cube. · 9 min
- 5 Splitting the middle term To factor x² + bx + c, find two numbers that add to b and multiply to c. · 9 min
- 6 Checkpoint: squares, cubes and the first split A graded check on the first five ideas: a cut-down square, one square from another, nine pieces, a cube, and the pair with two jobs. · 6 min
- 7 A number in front of the square With a number in front, the pair multiplies to first times last. Then group. · 9 min
- 8 What may be cancelled A top and bottom may lose only a shared factor, never a term that is added on. · 9 min
- 9 Adding two of them Add two algebraic fractions like number fractions: one shared bottom, then the tops. · 8 min
- 10 Proposing one of your own One disagreement settles a claim. Opening both sides out proves an identity. · 9 min
- 11 Checkpoint: coefficients, cancelling and testing A graded check on the last four ideas: a number in front, what may be struck out, adding two expressions, and what settles a claim. · 6 min
- 12 A square with two letters and numbers Square each part. The middle is twice their product, with the sign between the parts. · 9 min
- 13 Two cubes, one bracket x³ − y³ and x³ + y³ each split into two brackets. · 9 min
- 14 Squares by a round-number shortcut Write a² as (a + b)(a − b) + b². Pick b to make a factor round. · 8 min
- 15 The big picture Twelve ideas, tied back together. · 6 min
- 16 Track quiz Cheat-sheet table and thirteen questions, one per idea. · 10 min
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