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Derive the Three-Variable Cubic Identity

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Exploring Algebraic Identities · Cubic identities · 3:20

You'll learn: Expand and cancel to link a sum factor to x³+y³+z³−3xyz.

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Derive the Three-Variable Cubic Identity

3:20

Playing

Derive the Three-Variable Cubic Identity

You'll learn: Expand and cancel to link a sum factor to x³+y³+z³−3xyz.

Now playing

Same topic

Cubic identities

8

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.
Factor a Sum or Difference of Two Cubes
3:24
Factor a Sum or Difference of Two Cubes
You'll learn: Multiply the proposed factors and observe cancellation of mixed terms.
Does x−y Also Divide Fourth and Fifth Power Differences?
3:21
Does x−y Also Divide Fourth and Fifth Power Differences?
You'll learn: Extend the chapter’s factor pattern using known identities and multiplication.
Find a Sum of Cubes Without Finding the Three Numbers
3:32
Find a Sum of Cubes Without Finding the Three Numbers
You'll learn: Combine the square-of-three-terms identity with the cubic identity.

Next topic

Rational algebraic expressions

3

Factor First, Then Cancel Common Factors
3:31
Factor First, Then Cancel Common Factors
You'll learn: Simplify a rational expression by complete factorisation.
Use Square and Cube Identities in Rational Expressions
3:59
Use Square and Cube Identities in Rational Expressions
You'll learn: Recognise powers and factor denominator quadratics before simplifying.
Simplify Products of Quadratics and Fourth Powers
4:03
Simplify Products of Quadratics and Fourth Powers
You'll learn: Combine several identities and cancel only verified non-zero factors.

Next topic

Dimensions and area applications

4

Recover a Rectangle’s Dimensions from Its Tiles
3:32
Recover a Rectangle’s Dimensions from Its Tiles
You'll learn: Turn a square, strips and unit squares into a factored area expression.
Find Pool Dimensions by Factoring an Equation
3:30
Find Pool Dimensions by Factoring an Equation
You'll learn: Model a length difference and known area, then apply the zero-product property.
Factor Areas and Volumes to Suggest Dimensions
3:52
Factor Areas and Volumes to Suggest Dimensions
You'll learn: Interpret factors as possible positive dimensions and divide an area by a given width.
How Much Area Does a Path Around a Square Add?
3:29
How Much Area Does a Path Around a Square Add?
You'll learn: Subtract the original square area from the larger outside square.