How do you factor #90a^2 b^2 +45ab+10#?

1 Answer
Jan 27, 2017

Answer:

Complete the square to find:

#90a^2b^2+45ab+10 = 5/8(12ab+3-sqrt(7)i)(12ab+3+sqrt(7)i)#

Explanation:

#8/5(90a^2b^2+45ab+10) = 144a^2b^2+72ab+16#

#color(white)(8/5(90a^2b^2+45ab+10)) = (12ab)^2+2(12ab)(3)+3^2+7#

#color(white)(8/5(90a^2b^2+45ab+10)) = (12ab+3)^2-(sqrt(7)i)^2#

#color(white)(8/5(90a^2b^2+45ab+10)) = (12ab+3-sqrt(7)i)(12ab+3+sqrt(7)i)#

So:

#90a^2b^2+45ab+10 = 5/8(12ab+3-sqrt(7)i)(12ab+3+sqrt(7)i)#