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Expanding Brackets - Practice Worksheet and Examples

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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

456


<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 + 3)(x + 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 + b)² is equivalent to (a + b)(a + b) and should be expanded as such.

Example: For (3x + 2)²:

  • Rewrite as (3x + 2)(3x + 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

View

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 3(2x + 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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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

456

 

10/9

 

Maths

17


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

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 + 3)(x + 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

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 + b)² is equivalent to (a + b)(a + b) and should be expanded as such.

Example: For (3x + 2)²:

  • Rewrite as (3x + 2)(3x + 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

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 3(2x + 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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.