Can someone please help me with these math problems?

Question

1.) under what conditions does √x^2+y^2=x+y
2.) How do I ind the perimeter of a rectangle when the length is
3+6√2yd and the width is √8yd
3.) Find each product
(x+3)(x+8)
(y-2)(y+5)
(a-2)(a-9)

Answer 1

Hello Skymei!
I'll help you with problem 3! I want to show you how, but I want you to watch carefully and do the others yourself, okay? When there are numbers inside parenthesis like these, you use what is called the FOIL method! FOIL means First, Outer, Inner, Last! Watch and I'll do the 1st one:
(x+3)(x+8) = x^2+8x+3x+32 multiplying the First,Outer,Inner,Last
=x^2+11x+32 combining like factors (the answer!

Answer 2

#1. Square both sides, and you'll find that it's a NECESSARY condition for 2xy to be 0. That's equivalent to at least one of x or y being equal to 0.

However, that's not probably SUFFICIENT, if the most common definition of square root is being used. It is also necessary that neither of x nor y is negative.

#2. Just add twice the length to twice the width.

Simplifying at the end will turn out to be easier if the FIRST thing you do is say the square root of 8 is 2 times the square root of 2.