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$(2 + 3x) * (4 + 5x) = 2(4 + 5x) + 3x(4 + 5x)$

I don't get it. What do I do?

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This is a consequence of the distributive property of arithmetic operations: $(a+b)\cdot c = a\cdot c + b \cdot c$. – lhf Sep 25 '11 at 16:19
Suppose you put $x = 10$ so that the sum becomes $32 \times 54$. I hope you can see that you can compute this by splitting it up as $30 \times 54 + 2 \times 54$ - with a little jiggling of the order of terms you get the same pattern as you have stated. This is an example of the distributive law, and putting $x$ instead of $10$ generalises from the case of numbers in the decimal system to a wide range of applications. – Mark Bennet Sep 25 '11 at 16:20
What are you trying to do? Are you asking if what you wrote is correct (it is, as others have already explained), or how to proceed further? – Ted Sep 25 '11 at 17:54
up vote 5 down vote accepted

The equation you have uses the law of distribution: $$a(b+c)= ab + ac$$ If you set $a=4+5x$, $b=2$ and $c=3x$, you get the equation in your question.

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