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Factor First, Then Cancel Common Factors

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Exploring Algebraic Identities · Rational algebraic expressions · 3:31

You'll learn: Simplify a rational expression by complete factorisation.

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Factor First, Then Cancel Common Factors

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Factor First, Then Cancel Common Factors

You'll learn: Simplify a rational expression by complete factorisation.

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Same topic

Rational algebraic expressions

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Use Square and Cube Identities in Rational Expressions
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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
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Simplify Products of Quadratics and Fourth Powers
You'll learn: Combine several identities and cancel only verified non-zero factors.

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Dimensions and area applications

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Recover a Rectangle’s Dimensions from Its Tiles
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Recover a Rectangle’s Dimensions from Its Tiles
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Find Pool Dimensions by Factoring an Equation
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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
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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?
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How Much Area Does a Path Around a Square Add?
You'll learn: Subtract the original square area from the larger outside square.
A Number Plus Its Reciprocal: Use Factorisation
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A Number Plus Its Reciprocal: Use Factorisation
You'll learn: Clear a non-zero denominator, factor the quadratic and check both solutions.

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Chapter challenge problems

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Two Given Linear Factors Constrain a Quadratic
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Two Given Linear Factors Constrain a Quadratic
You'll learn: Use the stated factors to compare coefficients and prove a relationship.
Use a Sum and Pairwise Products in a Cubic Identity
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Use a Sum and Pairwise Products in a Cubic Identity
You'll learn: Express the second factor using the square-of-a-sum identity.
Why Is n³−n Always Divisible by Six?
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Why Is n³−n Always Divisible by Six?
You'll learn: Factor into three consecutive integers and reason about divisibility.
Evaluate Cubic Expressions from a Given Relationship
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Evaluate Cubic Expressions from a Given Relationship
You'll learn: Use a three-variable cubic identity to avoid finding individual variable values.

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Chance, randomness and the probability scale

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Probability Measures How Likely Something Is
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Probability Measures How Likely Something Is
You'll learn: Introduce uncertainty and likelihood using the chapter’s everyday questions.
Know What Could Happen Without Knowing What Will Happen
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You'll learn: Explain random experiments, individual trials and possible outcomes.
Why Can a Coin Toss Be a Fair Way to Decide?
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Why Can a Coin Toss Be a Fair Way to Decide?
You'll learn: Connect fairness to a symmetric coin and an unbiased random toss.
Read the Probability Scale from Zero to One
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You'll learn: Place impossible, less likely, even-chance, more likely and certain events on a scale.