Finite Product

Algebra Level 1

What is this equal to?:


The answer is 0.

César Castro by César Castro , 20, Honduras

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1 solution

Vilakshan Gupta
Mar 28, 2018

( a − k ) ( b − k ) ( c − k ) ⋯ ( k − k ) ⏟ 0 ⋯ ( x − k ) ( y − k ) ( z − k ) = 0 \large (a-k)(b-k)(c-k)\cdots\underbrace{(k-k)}_{0}\cdots(x-k)(y-k)(z-k)=\boxed{0}

5 Helpful 0 Interesting 1 Brilliant 0 Confused

Is there another way to find that it is 0. For example, expanding the whole product. I know it may come out as tedious, but is there?

César Castro - 3 years, 2 months ago

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Consider moving the (k-k) term to the front, then expanding out all of the other brackets. Then when you multiply through the (k-k) bracket you'll get each term times k and each term times -k, and so all the terms will cancel out.

Joseph Newton - 3 years, 2 months ago

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Cool! Thanks!

César Castro - 3 years, 2 months ago

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