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Why the Square Identity Also Works for Negative Numbers

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Exploring Algebraic Identities · Understanding and proving identities · 3:20

You'll learn: Move from area pictures to a distributive proof valid for signed and rational values.

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Why the Square Identity Also Works for Negative Numbers

3:20

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Why the Square Identity Also Works for Negative Numbers

You'll learn: Move from area pictures to a distributive proof valid for signed and rational values.

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Same topic

Understanding and proving identities

6

Three Consecutive Squares Always Give Two
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Three Consecutive Squares Always Give Two
You'll learn: Explore the opening square-number calculation and formulate the observed pattern.
An Identity Is an Equation True for Every Allowed Value
3:27
An Identity Is an Equation True for Every Allowed Value
You'll learn: Distinguish an identity from an equation holding only for certain inputs.
Build the Square of a Sum from Four Pieces
3:13
Build the Square of a Sum from Four Pieces
You'll learn: Partition a square of side a+b into a², b² and two ab rectangles.
When Is the Square of a Sum Bigger Than the Sum of Squares?
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When Is the Square of a Sum Bigger Than the Sum of Squares?
You'll learn: Use the sign of 2ab to compare (a+b)² with a²+b².
Square a Binomial with Coefficients and Fractions
3:30
Square a Binomial with Coefficients and Fractions
You'll learn: Identify the complete expressions playing the roles of a and b and expand correctly.
Use Nearby Round Numbers to Calculate Squares
3:25
Use Nearby Round Numbers to Calculate Squares
You'll learn: Choose a convenient additive split and evaluate with (a+b)².

Next topic

Perfect-square factorisation

6

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
3:23
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
3:25
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
3:40
Square Numbers Just Below a Round Number
You'll learn: Use (a−b)² to make subtraction-based calculations efficient.
Prove the Consecutive-Squares Pattern
3:20
Prove the Consecutive-Squares Pattern
You'll learn: Express the three squares using n−1,n,n+1 and simplify.

Next topic

Three-term squares and difference of squares

3

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.