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Assuming that 3u + v neq 0, simplify (54u^2 v + 18uv^2)(9u + 3v).

 May 2, 2023
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Assuming that \(3u + v \neq 0\), simplify \((54u^2 v + 18uv^2)(9u + 3v)\).

 

Multiply using FOIL to get \(486u^3v+162u^2v^2+162u^2v^2+54uv^3\).

We can then combine like terms to get \(486u^3v+324u^2v^2+54uv^3\).

If you like, you can factor out \(54uv\) to get \(54uv(9u^2+6uv+v^2)\).

Then you can note that \((9u^2+6uv+v^2)=(3u+v)^2\) and make the expression \(54uv(3u+v)^2\).

We could also have arrived at this by factoring common terms out of each binomial at the start.

Hope this is helpful!

 May 2, 2023

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