Find each product. Assume all variables represent positive real n...

Question

Find each product. Assume all variables represent positive real numbers. (x+x^1/2)(x-x^1/2)

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression. We have parentheses three Y minus Y to the 1/6 and parentheses times new parentheses three Y plus Y to the 1/6. And we are asked to find the product or to multiply these two sets of parentheses by each other. Well normally we would start with the foil process first plus the Outsides plus the insides plus the last. But we notice here that the first term in each set of parentheses is the same. They're both three Y and the second term inside of both sets of parentheses are the same. They're both Y to the 1/6. The only thing that's different is that one is minus and one is plus and we recognize that this is a special product, we have x minus Y times X plus y. And we know from previous lessons that that is equal to x squared minus Y squared. So we can identify which ones are are wise and which are our exes and then plug them in to the right hand side of the formula. And then we can skip that whole foil process. So the exes are what come first in each set of parentheses, the X is here, R three Y and the Y is what comes second in each set of parentheses. The y here is Y to the 1/6 and now we can plug those in for the right hand side of the equation and then simplify. So for X squared that will be three Y squared minus and instead of why square? This will be why to the 1/6 squared. Now we can simplify so we need to distribute this squared to both the coefficient and the variable and the parentheses. So we have to square three. That is 93 squared is nine and why squared is y squared minus. And now we've got a variable with an exponent raised to another exponent. And we have when we have an exponent raised to an exponent we are going to multiply the exponents. So this will be why raised to the 1/6 times two. Well 1/6 times two equals 2/6 which reduces to one third. So we've got nine y squared minus why raised to the one third. We look at our answer choices and this matches with answer choice C. Well done. We'll catch you on the next one.

Find each product. Assume all variables represent positive real numbers. (x+x^1/2)(x-x^1/2)

Key Concepts

Polynomial Multiplication

Exponents and Radicals

Factoring and Simplifying Expressions

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