Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

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Ruby

02/04/2023

Maths

Expanding brackets

Subjects

Maths

Algebra

Algebraic expressions

Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

Expanding brackets is a fundamental algebraic operation that involves multiplying terms inside parentheses by terms outside. This process is crucial in simplifying expressions and solving equations. Expanding brackets requires careful attention to the rules of multiplication and distribution, especially when dealing with multiple terms or nested brackets. Students learning this concept should practice with various expanding brackets examples to gain proficiency.

Key points:

Distribute the outer term to each term inside the brackets
Pay attention to signs when multiplying
Combine like terms after expansion
Be cautious with special cases like squaring binomials

02/04/2023

math
Expanding brackets.
Example
5 (od + 4) + 3 (200 +1)
= 5x +20 + 6x + 3
=11x +23.
F
Example 2
x (3x +4)
= 3x² + 4+ x
4
Example
(x + 2) (x

Advanced Expanding Brackets Techniques

This page delves into more complex examples of expanding brackets, including scenarios with higher degree polynomials and multiple sets of brackets.

The first example demonstrates expanding brackets with a quadratic term:

$x + 2$ $x² + x + 3$ = x³ + 3x² + 5x + 6

Highlight: When expanding brackets with higher degree terms, be careful to correctly multiply the exponents.

The page then shows an example with two sets of brackets, each containing multiple terms:

$2x - 1$ $7x² + x - 5$ = 14x³ + 2x² - 10x - 7x² - x + 5 = 14x³ - 5x² - 11x + 5

This example illustrates the importance of methodically multiplying each term and carefully combining like terms.

Example: $3x + 1$ $x + 1$ + 2 $x² - 5$ = 3x² + 5x² + 4x - 9

This problem combines expanding brackets with additional operations, demonstrating how these skills are applied in more complex algebraic expressions.

The page concludes with two more examples:

$2x - 5$ $3x + 1$ = 6x² - 13x - 5

$x - 4$ $x² + x - 2$ = x³ + x² - 2x - 4x² - 4x + 8 = x³ - 3x² - 6x + 8

Vocabulary: Polynomial - An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication operations.

These final examples reinforce the techniques for expanding double brackets and handling more complex algebraic expressions.

Highlight: Practice is key to mastering the skill of expanding brackets. Use expanding brackets worksheets and expanding brackets examples for algebra practice to improve your proficiency.

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Subjects

Maths

Algebra

Algebraic expressions

Maths

•

2 Apr 2023

•

2 pages

Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

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Advanced Expanding Brackets Techniques

This page delves into more complex examples of expanding brackets, including scenarios with higher degree polynomials and multiple sets of brackets.

The first example demonstrates expanding brackets with a quadratic term:

$x + 2$ $x² + x + 3$ = x³ + 3x² + 5x + 6

Highlight: When expanding brackets with higher degree terms, be careful to correctly multiply the exponents.

The page then shows an example with two sets of brackets, each containing multiple terms:

$2x - 1$ $7x² + x - 5$ = 14x³ + 2x² - 10x - 7x² - x + 5 = 14x³ - 5x² - 11x + 5

This example illustrates the importance of methodically multiplying each term and carefully combining like terms.

Example: $3x + 1$ $x + 1$ + 2 $x² - 5$ = 3x² + 5x² + 4x - 9

This problem combines expanding brackets with additional operations, demonstrating how these skills are applied in more complex algebraic expressions.

The page concludes with two more examples:

$2x - 5$ $3x + 1$ = 6x² - 13x - 5

$x - 4$ $x² + x - 2$ = x³ + x² - 2x - 4x² - 4x + 8 = x³ - 3x² - 6x + 8

Vocabulary: Polynomial - An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication operations.

These final examples reinforce the techniques for expanding double brackets and handling more complex algebraic expressions.

Highlight: Practice is key to mastering the skill of expanding brackets. Use expanding brackets worksheets and expanding brackets examples for algebra practice to improve your proficiency.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Expanding Brackets: Basic to Advanced Examples

This page introduces the concept of expanding brackets in algebra, providing a range of examples from simple to complex. Expanding brackets is a crucial skill in algebra, used to simplify expressions and solve equations.

Definition: Expanding brackets means multiplying the term outside the brackets by each term inside, then combining like terms.

The page starts with a simple example:

5 $x + 4$ + 3 $2x + 1$ = 5x + 20 + 6x + 3 = 11x + 23

This example demonstrates the basic process of distributing the outside term to each term inside the brackets, then combining like terms.

Example: x $3x + 4$ = 3x² + 4x

This shows how to expand when the outside term is a variable.

The page then progresses to more complex examples, including expanding double brackets:

Example: $x + 2$ $x + 5$ = x² + 7x + 10

This illustrates the FOIL method $First, Outer, Inner, Last$ for expanding double brackets, which is a key technique in expanding double brackets.

Highlight: When expanding double brackets, remember to multiply each term in the first bracket by each term in the second bracket.

The page also includes examples with negative terms:

6x $-2 + 3$ = -12x + 18x = 6x

$-x + 6$ $3x - 5$ = -3x² + 23x - 30

These examples emphasize the importance of careful sign management when expanding brackets with negative terms.

Vocabulary: FOIL - A method for expanding double brackets, standing for First, Outer, Inner, Last.

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Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

Advanced Expanding Brackets Techniques

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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.

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

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

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

Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

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Advanced Expanding Brackets Techniques

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Expanding Brackets: Basic to Advanced Examples

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