Question

Rewrite:
1. (x/2 +y^2)^2
2. 12xy + 4x^2+9y^2
Also brief explain the step to getting your answer?

Answer 1

1. Use the FOIL method for multiplying polynomials (First, Outside, Inside, Last)
(x/2 + y^2)^2
= (x/2 + y^2) * (x/2 + y^2)
= (1/4)*x^2 + (1/2)*x*y^2 + (1/2)*x*y^2 + y^4
= (1/4)*x^2 + x*y^2 + y^4

2. Here you have to do the opposite of what you did in problem 1. There's an x^2 and a y^2, so I know that it will have to take the form (a*x + b*y)^2, where a and b are some numbers. Since we have 4x^2, I will guess that a = 2, since 2^2 = 4. I will also guess that b = 3, since 3^2 = 9. The answer is then (2x + 3y)^2. If we expand this out using the FOIL method, we see that we get the same thing, including the 12xy.

Answer 2

Thanks