# Thread: Multiplying out brackets containing multiplication

1. ## Multiplying out brackets containing multiplication

Apologises in advance if i'm being a bit thick, or this has been answered before, my searches on this forum and google were unsuccessful.
My problem is that I'm trying to find the rule for expanding brackets which contain multiplied variables. I've found hundreds of examples with addition and subtraction, but no multiplication...which I thought was a bit odd.

Examplea*b)(x*y)

How would this be expanded to remove the brackets? I have a feeling theres a few conditions such as like bases. My specific problem involves terms that are constants raised to a variable power (plus or minus a constant).

2. Originally Posted by NitrousUK
Apologises in advance if i'm being a bit thick, or this has been answered before, my searches on this forum and google were unsuccessful.
My problem is that I'm trying to find the rule for expanding brackets which contain multiplied variables. I've found hundreds of examples with addition and subtraction, but no multiplication...which I thought was a bit odd.

Examplea*b)(x*y)

How would this be expanded to remove the brackets? I have a feeling theres a few conditions such as like bases. My specific problem involves terms that are constants raised to a variable power (plus or minus a constant).

Hi NitrousUK,

If I assume your little purple frown guy is hiding one of your parentheses, I am reading:

$\displaystyle (ab)(xy)$

All the bases are different here, so the product is simply:

$\displaystyle abxy$

These factors can be put in any order since multiplication is commutative.

3. Thanks for the quick response!
Sorry I wasnt clear with my example. It should of read (a^x a^y)(a^w a^z)
The problem im dealing with involves the same bases but raised to a variable power.

Thanks!

4. Originally Posted by NitrousUK
Thanks for the quick response!
Sorry I wasnt clear with my example. It should of read $\displaystyle \textcolor{red}{(a^x a^y)(a^w a^z)= (a^{x+y})(a^{w+z}) = a^{x+y+w+z}}$
The problem im dealing with involves the same bases but raised to a variable power.

Thanks!
...

5. Thanks!
However I see I'm missing out crucial info in my example. I'll use the same example that i'm stuck on, it's more complicated than the original question but multiplication of different bases inside two brackets was where i stumbled: $\displaystyle a^{n-1}b^{n+1}+b^{n-1}a^{n+1}-2(a^nb^n)=a^{n-1}b^{n-1}(b^2+a^2-2*a*b)$

I can't seem to see the steps/rules involved in getting from the first equation to the second.

6. Originally Posted by NitrousUK
Thanks!
However I see I'm missing out crucial info in my example. I'll use the same example that i'm stuck on: $\displaystyle a^{n-1}b^{n+1}+b^{n-1}a^{n+1}-2(a^nb^n)=a^{n-1}b^{n-1}(b^2+a^2-2*a*b)$

I can't seem to see the steps/rules involved in getting from the first equation to the second.
exponent review ...

note that $\displaystyle a^{n-1} \cdot a^2 = a^{(n-1)+2} = a^{n+1}$

also ...

note that $\displaystyle a^{n-1} \cdot a = a^{(n-1)+1} = a^n$

left side expression is $\displaystyle a^{n-1}b^{n+1}+b^{n-1}a^{n+1}-2(a^nb^n)$

now note that each of the three terms on the left side have the following factors in common ...

$\displaystyle a^{n-1}$ and $\displaystyle b^{n-1}$ ...

factor these two out ...

$\displaystyle a^{n-1}b^{n-1}[b^2+a^2-2(ab)]$