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Prove the Consecutive-Squares Pattern

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Exploring Algebraic Identities · Perfect-square factorisation · 3:20

You'll learn: Express the three squares using n−1,n,n+1 and simplify.

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Prove the Consecutive-Squares Pattern

3:20

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Prove the Consecutive-Squares Pattern

You'll learn: Express the three squares using n−1,n,n+1 and simplify.

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Same topic

Perfect-square factorisation

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Read a Perfect Square Backwards
3:27
Read a Perfect Square Backwards
You'll learn: Recognise a²+2ab+b² and write its repeated factor.
Take Out a Common Factor Before Looking for a Square
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Take Out a Common Factor Before Looking for a Square
You'll learn: Extract a common factor to expose a simpler perfect-square expression.
Derive the Square of a Difference by Substitution
3:19
Derive the Square of a Difference by Substitution
You'll learn: Replace b with −b in the square-of-a-sum identity.
See the Square of a Difference as an Area
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See the Square of a Difference as an Area
You'll learn: Remove the two appropriate rectangles from the larger square.
Square Numbers Just Below a Round Number
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Square Numbers Just Below a Round Number
You'll learn: Use (a−b)² to make subtraction-based calculations efficient.

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Three-term squares and difference of squares

6

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
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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.
Rearrange a Square to Reveal a Difference of Squares
3:31
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.

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

1

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.