Sat math question: if a ^2+b^2=258, what is the value of (a+b)^2+(a-b)^2? ?
explain how you arrived at your answer. you!

516

Step-by-step explanation:

Let's start with the value first to see if we can use to help find it's value:

I'm going to use the formula to expand both:

Combining like terms:

Factoring the 2 out:

Plug in 258 for the :

Perform the multiplication:

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Another way:

Find values for and that satisfy:

The easiest solution you might see is .  This works because the square of is 258.

So now you just plug:

with being and being 0 into your calculator or if you are good at simplifying things without you can do that with this problem:

This would have worked for any pair satisfying .

I wanted to show this last strategy just in case you haven't been exposed to expanding squared binomials with foil or the formula I mentioned earlier.