Question

Simplify the following expression.

(2x 2y 4)3
Help Please I have my reasons why I don't understand this.

Answer 1

Is that supposed to be
\[(2x*2y*4)^3\]?

Answer 2

Yes.

Answer 3

Okay. Do you know that \[(ab)^n = a^nb^n\]?

Answer 4

No I don't know that.

Answer 5

Okay. here's how you can think of that. Let's say you have \(3^4\). That means you are multiplying 3 together 4 times: \(3*3*3*3\) With me so far?

Answer 6

Yes.

Answer 7

Okay, let's say we have \(6^4\): \(6^4= 6*6*6*6\) right?

Answer 8

Mhm.

Answer 9

But we can also write 6 as 2*3, so we could write \[6^4 = (2*3)^4 = (2*3)*(2*3)*(2*3)*(2*3)\]and that we can rewrite as \[2*2*2*2*3*3*3*3 = 2^4*3^4\]

Answer 10

Okay.

Answer 11

So, for your problem, you can just take each thing inside the parentheses, raise it to the 3rd power, and then combine them all by multiplying. Try it and tell me what you get.

Answer 12

list the options?

Answer 13

6x6y12
8x5y7
8x6y12
8x8y64

Answer 14

Uhm Probably won't be close . Lol.

Answer 15

Let's work through it. First thing inside the parentheses is a 2. What is \(2^3\)?

Answer 16

8x6y12?

Answer 17

okay, if there are exponents, write a ^ in front of them.

Answer 18

for example, \(3^4\) would be written 3^4 (even better would be to use the equation editor, but I'll settle for the ^)

Answer 19

\[8x ^{2}6y ^{12}\]

Answer 20

Okay, so the original is supposed to be \((2x^2y^4)^3\)? You told me it was something else earlier!

Answer 21

Ughh I'm confused now.

Answer 22

If the original problem, correctly notated, is to simplify \((2x^2y^4)^3\), then \(8x^6y^{12}\) is the correct answer.

Answer 23

I meant to say the exponent 6, The two was a typo.

Answer 24

\[2^3 = 8\]
\[(x^2)^3 = x^{2*3} = x^6\]
\[(y^4)^3 = y^{4*3} = y^{12}\]
all of them multiplied together is \(8x^6y^{12}\)

Answer 25

Okay Thank you.

Answer 26

Sorry about the confusion, but it could have been avoided had the problem been clearly stated up front :-) Got another to do? no extra charge :-)

Answer 27

Actually I do.

Answer 28

great, let's give it a shot.

Answer 29

Find the product.

\[(m - 5)^{2}\]

Answer 30

Okay, you know how to multiply polynomials, I hope?
\[(m-5)^2 = (m-5)(m-5)\]

Answer 31

You hoped wrong. Lol I'm all new to this.

Answer 32

Okay, well, here's the lightning fast lesson in polynomial multiplication :-)

Answer 33

Okay :b

Answer 34

Do you know the distributive property of multiplication?

\(a(b+c) = ab + ac\)

Answer 35

Right?

\(3*15 = 45\)
\(3*(10+5) = 3*10 + 3*5 = 30 + 15 = 45\)

Answer 36

Agreed?

Answer 37

Agree.

Answer 38

Okay. that's all there is to it :-)

\[(a+b)(c+d) = a(c+d) + b(c+d) = ac + ad + bc + bd\]
In other words, each component of the first polynomial gets multiplied by each component of the second polynomial, and then you add up the pieces.

Here's an example with just numbers:
\[12*25 = (10+2)(20+5) = 10*20 + 10*5 + 2*20 + 2*5 \]\[= 200 + 50 + 40 + 10 = 300\]

So, let's try one with some symbols in there:
\[(x+1)(x+2) = \] (you tell me)

Answer 39

Uhmm

Answer 40

Here, I'll break it down a bit more:

\[(x+1)(x+2) = x(x+2) + 1(x+2)\]again by the distributive property

Answer 41

Can you start me off?

Answer 42

(x+1)(x+2=(1x+2x)+(1x+2) ?? Hopefully.

Answer 43

so now we distribute again:
\[x(x+2) + 1(x+2) = x*x + x*2 + 1(x+2) = x*x + x*2 + 1*x + 1*2\]
\[x*x = x^2\]so that becomes
\[x^2 + 2x + 1x + 2\]and now we combine the like terms:
\[x^2+3x+2\]

Answer 44

\[4x ^{2}+2\] ??

Answer 45

No, you can't add \(x^2 + 3x\) because they have different exponents. Just like 10 + 1 doesn't equal 20...

Answer 46

Dang it.

Answer 47

what to do after coming like terms?

Answer 48

combing*

Answer 49

I'm trying to learn I really am, It's so confusing I like just numbers .

Answer 50

after you've combined the like terms, you're done here. I have to go, so why don't we try your actual problem here:

\[(m-5)(m-5) = m(m-5) - 5(m-5)\] distributive property, now we do that again with each half of the expression on the right:
\[m(m-5) - 5(m-5) = m*m + m(-5) - 5*m -5(-5)\]

Answer 51

that gives us
\[m^2 - 5m -5m + 25\] (note that -5*-5 is +25, not -25!)
now if we go through and combine like terms:
\[m^2-5m-5m + 25 = m^2-10m+25\]so \(m^2-10m+25\) is the answer to the problem.

Answer 52

Your a freaking Genius. And a life saver Thanks.

Answer 53

You might get some value out of watching the Khan Academy videos on this stuff: https://www.khanacademy.org/math/algebra/polynomials

The ones I've looked at have generally been quite well done.