How do you multiply #(2ab+c^2)^2#?

1 Answer
Mar 4, 2018

Answer:

See a solution process below:

Explanation:

This is a special form of the quadratic equation:

#(color(red)(x) + color(blue)(y))^2 = (color(red)(x) + color(blue)(y))(color(red)(x) + color(blue)(y)) = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2#

Let #color(red)(x)# equal #2ab#

Let #color(blue)(y)# equal #c^2#

Substituting gives:

#(color(red)(2ab) + color(blue)(c^2))^2 =>#

#(color(red)(2ab) + color(blue)(c^2))(color(red)(2ab) + color(blue)(c^2)) =>#

#color(red)((2ab))^2 + (2 xx color(red)(2ab) xx color(blue)(c^2)) + color(blue)((c^2))^2 =>#

#4a^2b^2 + 4abc^2 + c^4#