PLEASE MATH EXPERT!
I am struggling thank you

Step-by-step explanation:

This is just a big multiplication, but it gets more simple when you break it into steps.

First consider . This multiplies out to

Next, . This is

Finally, . This is

Sum these three expressions together and you get

Step-by-step explanation:

(x² + 3y  + y²)(x² + 3y - y²)

= x²*(x² + 3y - y²)  + 3y*(x² + 3y - y²)  + y²((x² + 3y - y²)

= ( x²*x² + x²*3y - x²*y²)   +  [3y*x² + 3y*3y  - 3y*y²]   + {y²*x² + y²*3y  - y²*y²}

= x⁴ + 3x²y - x²y²   + 3x²y + 9y² - 3y³  + x²y² + 3y³ - y⁴

= x⁴  + 3x²y + 3x²y - x²y²  + x²y²  + 9y²  - 3y³ + 3y³ - y⁴

= x⁴ + 6x²y  + 0 + 9y² + 0 - y⁴

= x⁴ + 6x²y + 9y² - y⁴

Hint:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough