# Expanding Brackets: Math Help for 2nd Term Maths

• MHB
• raechelc93
In summary, a student is struggling with expanding a set of double brackets and a third term in the first set of brackets. They receive help and learn to distribute the terms in the second set of brackets to the terms in the first set, resulting in a more complex expression. They also learn to use the fact that multiplication distributes over addition to simplify the expression.
raechelc93
Hi there,

I am currently doing an Ext Math 1 subject and haven't really come across any issues when needing to expand brackets, however, have come across the below equation I can't quite figure out... Any help would be greatly appreciated!

$$(p-q+r^2)(3-(p^2+q^2))$$

The double brackets as well as the 3rd term in the first set of brackets has got me very confused and I can't seem to figure out how to even start with this one.

you’ve posted an expression, not an equation (there is no equal sign)

$(p-q+r^2)(3-p^2-q^2)$

to expand, distribute the $p$, then the $-q$, and finally the $r^2$ to the three terms in the second set of parentheses ...

$3p-p^3-pq^2 -3q + p^2q +q^3 +3r^2 -p^2r^2 -q^2r^2$

note the expanded expression is less “simplified” than the original factored expression ... expanding doesn’t always yield a better representation

Hi Skeeter,

Thanks for responding so quick! There are 2 sets of brackets within the second set though.. $(3-(p^2+q^2))$ would it still be the same process if this is the case?

It looks like you altered the second set of brackets from the orignal to get $(3-p^2-q^2)$ - how/why did you change it?

Nevermind - I just figured it out :)

$-(p^2+ q^2)$ is the same as $(-1)(p^2+ q^2)$ so we are multiplying $p^2+ q^2$ by -1. Using the fact that "multiplication distributes over addition", that is $(-1)(p^2)+ (-1)(q^2)= -p^2+ (-q^2)= -p^2- q^2$.

## What is the purpose of expanding brackets in math?

The purpose of expanding brackets is to simplify algebraic expressions by removing parentheses and combining like terms. This allows for easier manipulation and solving of equations.

## How do you expand brackets?

To expand brackets, you distribute the term outside the parentheses to each term inside the parentheses. Then, you combine like terms to simplify the expression.

## What are the rules for expanding brackets?

The rules for expanding brackets include:

• Distributive Property: a(b+c) = ab + ac
• Combining Like Terms: 2x + 3x = 5x
• Order of Operations: Always work inside parentheses first

## What are some common mistakes when expanding brackets?

Common mistakes when expanding brackets include:

• Forgetting to distribute the term outside the parentheses
• Forgetting to combine like terms
• Not following the correct order of operations

## How can I practice and improve my skills in expanding brackets?

You can practice expanding brackets by solving various algebraic equations and checking your answers. You can also find online resources and worksheets to help improve your skills. Additionally, working with a tutor or participating in a study group can also be beneficial.

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