MHB Expanding Brackets: Math Help for 2nd Term Maths

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The discussion revolves around expanding the expression \( (p-q+r^2)(3-(p^2+q^2)) \). The initial confusion stems from the presence of double brackets, but it is clarified that the expression can be simplified by distributing each term in the first bracket across the second. The correct interpretation of the second bracket is confirmed as \( (3-p^2-q^2) \), which is equivalent to \( 3 - (p^2 + q^2) \). The process involves recognizing that multiplying by -1 distributes across the terms in the parentheses. Ultimately, the user resolves their confusion and understands the distribution process involved in expanding the expression.
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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.
 
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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 $(-1)(p^2)+ (-1)(q^2)= -p^2+ (-q^2)= -p^2- q^2$.
 
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