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Why Squares of Numbers Ending in Five Have a Shortcut

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Exploring Algebraic Identities · Efficient numerical calculations · 3:42

You'll learn: Use the chapter’s rearranged square identity to explain the calculation pattern.

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Why Squares of Numbers Ending in Five Have a Shortcut

3:42

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Why Squares of Numbers Ending in Five Have a Shortcut

You'll learn: Use the chapter’s rearranged square identity to explain the calculation pattern.

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Efficient numerical calculations

2

Multiply Numbers Equally Spaced Around a Convenient Centre
3:23
Multiply Numbers Equally Spaced Around a Convenient Centre
You'll learn: Use the difference-of-squares identity for products.
Choose the Identity That Makes the Calculation Easier
4:02
Choose the Identity That Makes the Calculation Easier
You'll learn: Compare two-term and three-term decompositions for a given square or product.

Next topic

Algebra tiles and quadratic factors

8

Multiply Two Linear Expressions with Algebra Tiles
3:13
Multiply Two Linear Expressions with Algebra Tiles
You'll learn: Build a rectangle from one x² tile, x tiles and unit tiles.
Arrange Tiles to Discover Two Factors
3:23
Arrange Tiles to Discover Two Factors
You'll learn: Reverse the area model to read dimensions from a quadratic.
Why Must the Two Numbers Have the Right Sum and Product?
3:19
Why Must the Two Numbers Have the Right Sum and Product?
You'll learn: Explain why splitting 7x as 3x+4x fits twelve unit tiles but 2x+5x does not.
Generalise the Product (x+a)(x+b)
3:15
Generalise the Product (x+a)(x+b)
You'll learn: Use tiles and distributivity to derive x²+(a+b)x+ab.
Multiply Linear Factors with Different x-Coefficients
3:26
Multiply Linear Factors with Different x-Coefficients
You'll learn: Generalise the rectangle model to non-monic factors.
Factor Quadratics with Positive and Negative Terms
3:27
Factor Quadratics with Positive and Negative Terms
You'll learn: Find signed number pairs and express monic quadratics as two linear factors.
Recover Missing Factors When the Leading Coefficient Is Not One
3:22
Recover Missing Factors When the Leading Coefficient Is Not One
You'll learn: Use coefficient matching or middle-term splitting on the chapter’s non-monic examples.
Two Ways to Combine Known Identities
3:19
Two Ways to Combine Known Identities
You'll learn: Compare expansion first with factoring a difference of squares first.

Next topic

Cubic identities

5

Derive the Cube of a Sum by Multiplication
3:15
Derive the Cube of a Sum by Multiplication
You'll learn: Multiply (a+b) by its squared expansion and collect like terms.
Build a Cube from Two Cubes and Six Cuboids
3:14
Build a Cube from Two Cubes and Six Cuboids
You'll learn: Visualise the cubic identity as a volume decomposition.
Derive the Cube of a Difference and Track Its Signs
3:32
Derive the Cube of a Difference and Track Its Signs
You'll learn: Substitute −b into the cube-of-a-sum identity.
Recognise a Perfect Cube in an Expanded Expression
3:31
Recognise a Perfect Cube in an Expanded Expression
You'll learn: Recover a repeated cubic factor from four terms.
Calculate Cubes Using Nearby Convenient Numbers
3:49
Calculate Cubes Using Nearby Convenient Numbers
You'll learn: Choose a sum or difference and apply a cubic identity.