Sheila's Responses in WyzAnt Answers

(2a + 4)^3 means (2a + 4)(2a + 4)(2a + 4)

Multiply the first two groupings together using FOIL:
(2a + 4)(2a + 4) =  4a^2 + 8a + 8a + 16
Combine like terms:  4a^2 + 16a + 16

Now take that answer and multiply by the third grouping using distributive property:

(4a^2 + 16a + 16)(2a + 4) =  8a^3 + 16a^2 + 32a^2 + 64a + 32a + 64

Combine like terms to get: 8a^3 + 48a^2 + 96a + 64

If you look closely at Nataliya D's answer, you'll see that multiplying each term in her grouping by the 8 out in front gives you the same answer.

Hi, Leanna.

In my Algebra class we are doing something similar to this.  Without the directions, it's hard to say if it's the same as our lesson.

Anyway, our book asks us to come up with possible number(s) to put in the blank so that you can factor the polynomial, 5x^2 + 11 x + blank.  What we did in our math class is to write out the two sets of (  )'s and try to figure out possibilities...

(5x + ___ )(x + ___ )

Somehow we need to make the outers and inners combine to give 11x.

If we try 1 and 1, it will be too small:

(5x + 1)(x + 1)
This multiplies to give 5x^2 + 5x + 1x + 1.  The outers and inners combine to give 6x (see, too small).

So how about 2 and 1?

(5x + 2)(x  + 1)
This multiplies to give us 5x^2 + 5x + 2x + 2, which is 5x^2 + 7x + 2 ... this is not right because our middle term is 7x.

So, how about trying 1 and 2?

(5x + 1)(x + 2) 
This multiplies to give us 5x^2 + 10x  + 1x  + 2.  This one will work because 10x and 1x combine to give you an 11x.  Ahah!

So, the answer to the blank in the original problem would be a positive 2

Hi, Clifford.

You're right when you say that you need to multiply the neg 5 by n and by 2.  But be careful with your signs...
-5 * n = -5n
-5 * 2 = -10 (not pos 10)

After you do that you multiply the second grouping by -1 (the one is "understood")
-1 * 3 = -3
-1 * 6n = -6n

Now your new equation looks like this:
-5n - 10 - 3 - 6n = -12n

Once you've taken care of the grouping symbols (the parentheses), you can simplify the left side by combining like terms:
-11n  - 13  = -12n

From here, get variable terms on one side and plain number (constant) terms on the other:
-11n  -  13  =  -12n
+12n              +12n 
   n    - 13    =    0

Now add 13 to both sides to get your answer:
n  - 13 =    0
   + 13    + 13
    n    =   13

Hope this helps.

Hi, Shanice.

I'm seeing your problem as:

y^3 z^6
y^5 z^6 

When simplifying fractions of this type, locate parts with like bases and subtract exponents.  The y's go together, and the z's go together.  

Y's:  5 - 3 = 2  So we have y^2 for the y-term.
Since y^5 is bigger, keep the answer below.

Z's: these are the same and cancel out to be an understood 1

So our answer is:

   1                                          .
 y^2

Hi, Allison.

I thought I'd throw in my two cents here too.

When I teach these type of problems (mixture story problems), I tell my students to look for two ideas: Quantity and Value.  These two ideas will create two equations for the story.

Quantity - answers the question, "How many do I have?"
In this problem we have 50 pounds of M&M's and trail mix combined.  So choose a letter to represent each snack (x can be the M&M's and y can be the trail mix).  

x + y = 50  ... see how easy it is to create the Quantity sentence?

Value - places value on each item in the mix
In this problem M&M's are worth $2.00 per pound, and the trail mix is worth $1.50 per pound.  So to start off, we will write 2.00 x  +   1.50 y  = something... the something is the party mix amount multiplied by its value of $1.80 per pound.  So here's my Value sentence:

2.00 x  +   1.50 y  =  1.80 (50)
2.00 x  +   1.50 y  =  90

Now that we have a Quantity sentence and a Value sentence, we can proceed with solving our system of equations.

       x +   y = 50
2.00 x + 1.50 y = 90

If we multiply the bottom one by 10, we can "get rid of the decimals," and we will get:
20x + 15y = 900

Okay, so now we have:

    x +    y = 50
20x + 15y = 900

From here, we may use one of three methods to find our answers: graphing (not too desirable - too difficult to maintain accuracy), substitution, and elimination.  My favorite method is elimination, but I can show you both substitution and elimination here.

Substitution

Solve the first equation for one of the variables... let's say we're solving for x:
x + y = 50
   - y       - y                             .
x       =  - y + 50

Now, put the expression we have for x into the other equation:

  20   x         +  15y = 900
20( - y + 50)  + 15y = 900
-20y  + 1000  + 15y  = 900
-5y  + 1000   =   900
      - 1000      - 1000
-5y      =  -100

-5y     =   -100
 -5             -5 

y = 20 (Trail Mix = 20 pounds)
x = 30 because 20 + 30 = 50

So, the person in the story should use 30 pounds of M&M's and 20 pounds of Trail Mix.

Elimination

   x +   y  =  50
20x + 15y = 900

Elimination is cool because you get to clear out one of the variables and work out an "easier" problem.
If we wish to eliminate the x's, multiply the top equation by negative 20:

-20x   - 20y   =   -1000
 20x   + 15y   =     900
           - 5y    =   -100

           - 5y    =   -100
             -5            -5

y = 20 (again)
And so x = 30 (again)

It's up to you which way you prefer to solve systems of equations (unless the directions on your homework or test tell you otherwise).

Hope this long-winded explanation made some sense to you.