ShmoopTube

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Here’s your shmoop du jour, brought to you by the difference of two squares.

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Sure, all squares have their differences…but we hope these two can work things out.

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If 9x2 - y2 = 15 and 3x - y = 3, what does 3x + y equal?

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The most important thing is to recognize that, in this

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problem, 9x squared minus y squared is a difference of two squares…

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…so “a squared minus b squared” can be factored into “a minus b times a plus b”.

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9x squared is 3x times 3x.

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So we can factor the first equation so it becomes (3x + y) times (3x - y) = 15.

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Then we give a little whistle and call over the second equation…which we can now substitute:

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(3x + y) times 3 = 15; then, dividing both sides by 3, we get 3x + y = 5.

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So our correct answer is 5. Good boy. Now…roll over.

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