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Rearrange a Square to Reveal a Difference of Squares

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Exploring Algebraic Identities · Three-term squares and difference of squares · 3:31

You'll learn: Relate a²−b² to a rectangle of sides a+b and a−b.

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Rearrange a Square to Reveal a Difference of Squares

3:31

Playing

Rearrange a Square to Reveal a Difference of Squares

You'll learn: Relate a²−b² to a rectangle of sides a+b and a−b.

Now playing

Same topic

Three-term squares and difference of squares

5

Square Three Terms by Grouping Two of Them
3:14
Square Three Terms by Grouping Two of Them
You'll learn: Derive (a+b+c)² from the two-term square identity.
Find All Nine Regions in a Three-Part Square
3:18
Find All Nine Regions in a Three-Part Square
You'll learn: Label the geometrical model and connect paired rectangles to cross terms.
Expand and Factor Three-Term Squares with Signs
3:36
Expand and Factor Three-Term Squares with Signs
You'll learn: Handle a negative term and reverse a six-term perfect-square expansion.
Test a Proposed Identity Before Accepting It
3:26
Test a Proposed Identity Before Accepting It
You'll learn: Use a counterexample or full expansion to test a claimed universal equality.
Read a Four-Square Identity from a Rearrangement
3:33
Read a Four-Square Identity from a Rearrangement
You'll learn: Translate the two rows of shapes into an algebraic relationship.

Next topic

Efficient numerical calculations

3

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.
Why Squares of Numbers Ending in Five Have a Shortcut
3:42
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.
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

7

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.