How do I use the bowtie method to multiply $(2x-27)(-x+15)$?

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The bowtie method seems like an easy concept to have down, but how is it used to multiply binomials such as $(2x-27)(-x+15)$?

Calculating the answer is not the problem, because I can get $(-2x^2+57x-405)$, I'm just not sure how to use this method to represent how to multiply the equation.

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1 Answer

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Well, if you don't have any problem multiplying out the product directly, then you don't need any bowtie mnemonics, and it would be pointless to spend effort on learning one.

That being said, you would draw something like

2x -27 |\ /| | X | |/ \|
-x 15

and then each of the lines in the bowtie corresponds to one term of the product. You get (in some order) $$ 2x\cdot(-x) + 2x\cdot 15 + (-27)\cdot(-x) + (-27)\cdot15 $$ Then you just need to rearrange and simplify in order to get the answer you already know!
(And all in all it's probably the same calculation you're already doing, just without the silly diagram to remind you which terms to multiply).

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