Can any of you help me... I just don't understand?

Question

Find the product.

1) -(1/2)y(2y^3 - 8)

2) 2y^2(3x + 5z)

3) a^4(3a^2 - 2a + 1)

You can show me the concept.

Answer 1

This is what you do

1)  you take -(1/2)y and multiply it by 2y^3 which is -y^3 then you multiply -(1/2)y by -8 which is +4y so your answer is -y^3+4y

2) same concept you take 2y^2 and multiply it by 3x which is 6(y^2)x and you multiply 2y^2 by 5z so you get 10(y^2)z. remember since you have different variables you can't combine them but you do multiply the coefficients. your answer should be 6(y^2)x+10(y^2)z

3) Once again it's done the same way a^4 times 3a^2. since they are the same variable when you multiply them together you add the exponents making it 3a^6 next is a^4 times -2a. Remember if there is no exponent shown it is then 1 so that will equal -2a^5 and finally it is a^4 times 1 which is a^4 so the answer is 3a^6 - 2a^5 + a^4. any more questions just email me.

Answer 2

sorry i missed school.

Answer 3

You distribute the first term (the part before the parentheses)  by multiplying it by each individual term in the paretheses.

Let's look at the first one. Now, another way to write it (that is easier to see over the computer is:

-.5y(2y^3-8)

So now you distribute the first term (and I used a minus between the terms because it was 2y^3 minus 8):

(-.5y*2y^3) - (-.5y*8)

Now you multiply within the paretheses

(-1y^4) - (-4y) = -y^4 + 4y

Hope that helps!

Answer 4

You need to do the stuff in the parenthesies first. The order of operations is very easy once you have it memorized. just remember the word "pemdas".

Parenthesies

Exponents

Multiplication/Division

Addition/Subtraction.

You always do what is in the parenthesies first. And even inside the parenthesies you still follow this order... So if you have exponents in parenthesies, solve those first.

Answer 5

19?

Answer 6

There are two ways I know of to go about learning to solve a question like this: regular distributive property or drawing rectangles.

1) I'm assuming that what's written there is supposed to represent the equivalent to -.5y(2y^3 - 8)?

Distributive: You take the outside term (in this case, your -1/2 y) and multiply it to the first term in the brackets; done that, you take the -1/2 y and multiply it to the next term in the brackets (in this case, -8). If you had more terms, you'd keep going one by one through the brackets.

This means you'd have -1/2 y times 2y^3 = -y^4.

And you'd have -1/2 y times - 8 = + 4.

Final answer: -y^4 + 4

NOTE: Some people find it easier to keep track of what they're doing by drawing a curved arrow from the top of the outside term to the top of the term they are about to multiply.

The other option I mentioned was using rectangles/boxes. For this, you'd draw a rectangle that is long vertically (not really long). Draw a horizontal line through the middle of the rectangle. On the top edge of the rectangle, write -1/2 y. On the left side of the top section, write 2y^3. On the left of the bottom section, write -8. Then you treat each sub-rectangle as an area to figure out:

-1/2 y times 2y^3 for the area of the top rectangle: gives -y^4. You write that in the rectangle.

-1/2 y times -8 gives you +4y. You write that in the bottom rectangle.

Final answer: -y^4 + 4y.

Same answer, slightly different approach. The rectangle ("box") method is good if you like a visual element or find it difficult to track which terms you've multiplied.

You would take the same approach for the other answers. Give it a shot and share your answers and we can tell you if they're correct.

Answer 7

what job would you use that in?

Answer 8

for the 1)answer is -16y^5

2)y^2(6x+10z)

3)a(3a^5-2a^4+1)