Question

If the quantity 4 times x squared times y squared plus 8 times x cubed times y to the fifth power all over 2 times x times y squared is completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent is completely simplified to 2xayb + 4xcyd, where a, b, c, and d represent integer exponents, what is the value of c?

Answer 1

            The statement "quantity 4 times x squared times y squared plus 8 times x cubed times y to the fifth power all over 2 times x times y squared" can be expressed as:

 (4x^2y^2 + 8x^3y^5) / 2xy^2

 In simplifying this expression, the steps are:

 1. Bring out the common factor of the numerator

 4x^2y^2 (1+2xy^3) / 2xy^2

 2. Cancel out the numerator and denominator

 2x(1+2xy^3)

 4. Expand again

 2x + 4x^2y^3

 This means that the exponents of a, b, c, d are:

 a = 1

b = 0

c = 2

d = 3