Question

what term should be added to 36a^2+49b^2 to make it a perfect square
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Answer 1

Answer:

Disregarding the clever "(x²+10x)² is a perfect square" , what you've basically been asked to do is to complete the square.

The simplest way to do this is by using the formula (x+a)² = x² + 2ax + a²

For example: x² + 10x.

Because the completed polynomial must be a square, it has to be equivalent to x² + 2ax + a².

So 2a = 10, or

a² = 25

We thus know that the completed quadratic polynomial equals x² + 10x + 25

The other exercises are solved exactly the same way. I won't do the boring mindless work of solving all of them.

hope this have helped you out a lot

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