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Single brackets: Expanding and factorising

Single brackets: Expanding and factorising

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Explainer Video

Tutor: Meera

Summary

Single brackets: Expanding and factorising

In a nutshell

A number or term can be multiplied by an expression in brackets. e.g. 2x(3x+2y)2x(3x+2y)2x(3x+2y). The term on the outside of the bracket should be multiplied by each term in the expression that is inside the brackets. This is called multiplying out single brackets. Some expressions can be put back into single brackets (factorised), by taking out a common factor from the expression.


Note: Be careful with negative signs inside the bracket, or with a negative term in front of the bracket.

​


Multiplying out single brackets

To multiply out brackets, multiply the number on the outside with each term on the inside of the bracket. You can use a multiplication grid to help.


Example 1

Multiply out 2(x+3)2(x+3)2(x+3).

Maths; Algebra; KS4 Year 10; Single brackets: Expanding and factorising


Use a multiplication grid to help.

​×\times×​​
​xxx​​
​ +3+3+3​​
​222​​
​2x2x2x​​
​666​​


Examples
​3(y+1)3(y+1)3(y+1)​​
​=3y+3= 3y+3=3y+3​​
​2x(x−5)2x (x-5)2x(x−5)​​
​=2x2−10x=2x^2 - 10x=2x2−10x​​
​3a(2b+5t)3a(2b+5t)3a(2b+5t)​​
​=6ab+15at=6ab+15at=6ab+15at​​
​−5x(3x−4y)-5x(3x-4y)−5x(3x−4y)​​
​=−15x2+20xy=-15x^2+20xy=−15x2+20xy​​
​3b(2c2+7d−3)3b(2c^2+7d-3)3b(2c2+7d−3)​​
​=6bc2+21bd−9b=6bc^2+21bd-9b=6bc2+21bd−9b​​



Factorise single brackets

To factorise single brackets, think about what is common in all the terms in the expression. This is the common factor. Keep the common factor on the outside of the bracket, and find the expression on the inside of the bracket.


Example 2

Factorise 3x+123x+123x+12.


​3x3x3x and 121212 both have a common factor of 333. So take the number 333 on the outside of the bracket. Then you need xxx, to multiply with 333 to get 3x3x3x, and +4+4+4 to multiply by 333 to get +12+12+12.

​​3x+12=3(x+4)‾3x+12 = \underline{3(x+4)}3x+12=3(x+4)​​


You can use a multiplication grid to help.

​×\times×​​
​xxx​​
​+4+4+4​​
​333​​
​3x3x3x​​
​+12+12+12​​


​

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Multiplying and dividing algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Single brackets: Expanding and factorising

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Single brackets: Expanding and factorising

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FAQs - Frequently Asked Questions

What is a common factor when factorising single brackets?

A common factor is a number or term that divides exactly into 2 or more terms in an expression. E.g. For the expression 3x+12, 3 divides into 3x exactly, and 12 exactly, so 3 is the common factor.

How do you factorise single brackets?

To factorise single brackets, think about what is common in all the terms in the expression. This is the common factor. Keep the common factor on the outside of the bracket, and find the expression on the inside of the bracket.

How do you multiply out single brackets?

To multiply out single brackets, make sure to multiply the term on the outside of the bracket with each term on the inside of the bracket.

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