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Expanding Brackets - Practice Worksheet and Examples

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Priyana

12/10/2022

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Expanding Brackets - Practice Worksheet and Examples

Expanding Brackets and double brackets in algebra is a fundamental mathematical concept that helps simplify expressions by multiplying terms inside and outside parentheses. This comprehensive guide covers single and double bracket expansion techniques, including the FOIL method and squared brackets.

  • Expanding single brackets involves multiplying each term inside the bracket by the term outside
  • The FOIL method (First, Outside, Inside, Last) is used for expanding double brackets efficiently
  • Squared brackets are rewritten as identical double brackets before expansion
  • Examples demonstrate how to combine like terms after expansion
  • Step-by-step solutions show proper algebraic manipulation techniques
...

12/10/2022

485

<p>The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the bra

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Page 2: The FOIL Method for Double Brackets

This page explains the systematic FOIL method for expanding double brackets, providing a structured approach to multiplication of binomial expressions.

Definition: FOIL stands for First, Outside, Inside, Last - representing the order of multiplication when expanding double brackets.

Example: When expanding x+3x + 3x+8x + 8:

  • First: x × x = x²
  • Outside: x × 8 = 8x
  • Inside: 3 × x = 3x
  • Last: 3 × 8 = 24
  • Combined result: x² + 11x + 24

Highlight: Double bracket expansion typically results in four terms initially, often combining to three terms after simplification.

<p>The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the bra

View

Page 3: Squared Brackets

This page covers the special case of squared brackets and demonstrates how to handle them in algebraic expressions.

Definition: A squared bracket a+ba + b² is equivalent to a+ba + ba+ba + b and should be expanded as such.

Example: For 3x+23x + 2²:

  • Rewrite as 3x+23x + 23x+23x + 2
  • Apply FOIL method
  • Result: 9x² + 12x + 4

Highlight: Always rewrite squared brackets as double brackets before expanding to ensure accurate results.

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3 pages

Expanding Brackets - Practice Worksheet and Examples

user profile picture

Priyana

@priya17262727

Expanding Brackets and double brackets in algebra is a fundamental mathematical concept that helps simplify expressions by multiplying terms inside and outside parentheses. This comprehensive guide covers single and double bracket expansion techniques, including the FOIL method and squared brackets.... Show more

<p>The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the bra

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Page 2: The FOIL Method for Double Brackets

This page explains the systematic FOIL method for expanding double brackets, providing a structured approach to multiplication of binomial expressions.

Definition: FOIL stands for First, Outside, Inside, Last - representing the order of multiplication when expanding double brackets.

Example: When expanding x+3x + 3x+8x + 8:

  • First: x × x = x²
  • Outside: x × 8 = 8x
  • Inside: 3 × x = 3x
  • Last: 3 × 8 = 24
  • Combined result: x² + 11x + 24

Highlight: Double bracket expansion typically results in four terms initially, often combining to three terms after simplification.

<p>The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the bra

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Page 3: Squared Brackets

This page covers the special case of squared brackets and demonstrates how to handle them in algebraic expressions.

Definition: A squared bracket a+ba + b² is equivalent to a+ba + ba+ba + b and should be expanded as such.

Example: For 3x+23x + 2²:

  • Rewrite as 3x+23x + 23x+23x + 2
  • Apply FOIL method
  • Result: 9x² + 12x + 4

Highlight: Always rewrite squared brackets as double brackets before expanding to ensure accurate results.

<p>The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the bra

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Page 1: Basic Bracket Expansion

This page introduces the fundamental concept of expanding single brackets in algebraic expressions. The process involves multiplying each term inside the brackets by the term outside.

Definition: Expanding brackets means multiplying each term inside the brackets by the term outside the brackets.

Example: In expanding 32x+52x + 5:

  • First multiply 3 × 2x = 6x
  • Then multiply 3 × 5 = 15
  • Final answer: 6x + 15

Highlight: When expanding multiple brackets in one expression, expand each bracket separately first, then group like terms, and finally simplify the expression.

Vocabulary: Like terms are terms that have the same variables raised to the same powers.

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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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