Question

factorize a2+b2 with explanation

Answer 1

a2+b2
a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab. 2. ( a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab. 3. ( a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Answer 2

Whereas #a^2-b^2 = (a+b)(a-b)# is very simple, to factor #a^2+b^2# requires the use of complex numbers.

If #i = sqrt(-1)# then

#(a+ib)(a-ib)#

#=a^2+iab-iab-i^2b#

#= a-i^2b#

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

#= a^2 + b^2#

So #a^2+b^2 = (a+ib)(a-ib)#, but there is no other factoring with real number coefficients.