Question

What is an example of a "sum of two squares" ?

Answer 1

a^2 + b^2 ?

Answer 2

yeah, but what is the factored form?

Answer 3

i don't see how u can simplify this further....
a^2 + b^2 = (a+b)^2 - 2ab........but this is not really simplifying it.
do u want an expression in variables or can u use actual values?

Answer 4

isnt it complex?

Answer 5

actual values

Answer 6

a + b
a - b
------
a^2 +ab
-ab -b^2
------------
a^2 - b^2

a difference of squares would be factored as conjugates

Answer 7

a sum of squares goes complex

Answer 8

oh. then its easy.
take a = 6, b = 8
so 6^2 + 8^2 = 36 + 64 = 100
is this what u're looking for?

Answer 9

well this was the quesion my teacher gave me:

Answer 10

Using complete sentences, compare and contrast the ways to factor the "sum of two squares" and the "difference of two squares." Provide an explanation and example of each, including any similarities and differences.

Answer 11

a + bi
a - bi
-------
a^2 +abi
-abi -b^2 i^2
----------------
a^2 -b^2 i^2


such that i^2 = -1, resulting in

a^2 -b^2(-1) = a^2 + b^2

Answer 12

oh. then follow @amistre64's solution.

Answer 13

follow it backwards.

Answer 14

okay