Monomials+vs.+binomials+Set+3

It is a common mistake among some algebra students to assume that (x+y)² = x²+ y², since (xy)²= x²y². What is the difference between these two problems? Give the rule for each, and also present a problem for each. Make it a little more challenging!

The difference between those two problems is that (x+y)^2 implies using FOIL and multiplying each variable by the other variables instead of having x^2*y^2. So, when it is a binomial, you must multiply each variable/number by each other one, but with monomials you just apply the exponent to each variable independent of any other variables.

Solve for x:

(6 + 4)^2 = x

[(5)(2)]^3 = x

-Hannah

But this really is not a true binomial as I would give one, since you did not have a variable. In each case, as Drew showed below, all you have to do is simplify inside the radicals first, and then there is no distinction between your first example and the second example. What about something that we have done this year, such as: simplify (3x⁵+y⁷)² and also, for contrast, simplify (3x⁵y⁷)²

(10)^2=x x=100

10^3=x x=1000

-TheHornDog Aka Drew