Somewhat homework help.

I had a mathematics test yesterday, and got the results back today. The quiz was on radicals, algebraic functions, and related. One question I got incorrect is now stumbling me.

Below is the question, then below that is the work I put in, the underlined step is the result I had:

Simply the following expressions.

  1. f) 4x(x-2)^2

=> 4x(x-2)^2
=> 4x(x^2-4)
=> 4x^3-16x

However, the instructor had marked it incorrect, and put in red the supposed correct answer:

4x^3 - 16x^2 + 16x

How the fuck is that the answer? I tried complaining to the instructor, and even gave proof:

If I substitute the variable (x) for 1, and solve for the question, and answer she gave; they do not equal.

  1. f) 4x(x-2)^2

=> 4(1-2)^2
=> 4

-. -) 4x^3 - 16x^2 + 16x

=> 4^3 - 16^2 + 16
=> 64 - 256 + 16
=> -176

Since 4 != -176, the answer she gave cannot be correct. Am I making a mistake, or am I right?

You’re wrong on both counts, I’m afraid. In the second part of your proof, you substituted x for 1. It should then look like this:

4x^3 - 16x^2 + 16x
=> 4(1)^3 - 16(1)^2 + 16(1)
=> 4(1) - 16(1) + 16(1)
=> 4

I think you may be getting confused about order of operations: exponents always come before multiplication. The original question is solved like this:

=> 4x(x-2)(x-2)
=> 4x(x^2 -2x -2x +4)
=> 4x(x^2 -4x +4)
=> 4x^3 -16x^2 +16x

Hope that helps.

Ah. That makes sense, thanks. Lock the thread if you wish.

Wow. Your math is completely wrong.

First off, in your “proof,” you completely misuse exponents. If you substitued 1 for x, it would be 4(1)^3 - 16(1)^2 + 16(1).
Now, we all (should) know 1 raised to any power is 1. So, we can simplify that to
4 - 16 + 16, which does indeed equal 4.

Secondly, her answer is right. Proof!
=> 4x(x-2)(x-2)
=>4x(x^2 - 4x + 4)
=> 4x^3 - 16x^2 + 16x

Your problem is you tried distributing the original exponent into the parantheses. You can’t just slide it in. You have to treat the entire object as being squared, so you have to multiply the object (x-2) by itself, which gives you x^2 - 4x + 4

Oh. Cid got it too. Yay. :slight_smile:

As Cid said, order of operations.

(a+b)^2 = a^2+2ab+b^2

It’s important to note that (a+b)^2 = (a+b)(a+b), a form you may be more familiar with.

Equations of the form (a+b)(c+d) must be multiplied in a special way. Traditionally students are taught to use the “FOIL” method or “CAT” method to do so, either of which you might recall from previous lectures. Using either method to multiply will give the result (a+b)(c+d) = ac+ad+bc+bd.

Because in this instance you have (a+b)(a+b), multiplying will give the result aa +ab+ba+bb which can be simplified as a^2+2ab+b^2.

PEMDAS -> Please Excuse My Dear Aunt Sally -> Parentheses Exponents Multiplication/Division Addition/Subtraction, for future reference.

…and great justice.

The mnemonic device taught in my schools was BFEDMAS. Which doesn’t make a phrase, but is Brackets, factorials, exponents, division, multiplication, addition, and subtraction.

BFEDMAS? That’s silly. Parentheses are used for the same reason as brackets, but parentheses are more common. And how much do you run into factorials? And I think most people intuitively realize that a unary operator (like the factorial symbol) has higher precedence than a binary operator.

It’s just plain BEDMAS. I don’t think you do factorials much in highschool math unless you’re taking Finite. Even then it’s only in combinations and permutations.

BEDMAS is just the incomplete of BFEDMAS. PEMDAS is the incomplete of PFEMDAS. I looked it up.

Just where did you look it up? This is what I got when I searched Wiki:

and this is what I got when I searched Google:

I found both BEDMAS and PEMDAS when I put those in the search engine,
so either you’re remembering wrong or your textbook has a typo.

The Wikipedia article for Order of Operations does mention factorials, Lex. PFEMDAS would be the correct order if we included F in the device. However, it’s such an obscure function for most people that we don’t include it. So, the textbook is just mentioning an obscure version of the one we all know and love.

I see. Thanks for clearing that up, 984.

If you press Ctrl and F on that Wikipedia page, and search for BFEDMAS, or PFEMDAS, it’s in the article. And the google link you gave directly points to that section in Wikipedia with BFEDMAS.

The point of that link was Google asking, “Did you mean to search for BEDMAS?” Meaning BFEDMAS isn’t that common a term.