Question

Identify the third term in the expansion of (7x – 2y)^3

Answer 1

7x^3-2y^3 so the 3rd term of expansion is 2

Answer 2

are you sure?

Answer 3

no lol

Answer 4

ask GT

Answer 5

whoose that?

Answer 6

he answerd 3 of my questions correctly

Answer 7

nice..I think edgeoftheearth is helping

Answer 8

This is a binomial theorem problem. The third term of (a+b)^3 would be ab^2, but we have 7x-2y instead of a+b. So it's going to be (7x)(-2y)^2, which reduces to 7x4y^2, which reduces to 28xy^2. Now we need to find the coefficient. Does that make sense so far?

Answer 9

aright

Answer 10

kind of

Answer 11

If we have (a+b)^3 the terms will be \[a ^{3}b^{0} +a ^{2}b^{1} + a^{1}b^{2} + a ^{0}b^{3}\]

If we look we can see a pattern. The first term (a) starts from the exponent (3 in this case) and goes down by 1 each term. The second term (b) starts at the exponent of 0 and increases by 1 each term.

Answer 12

See what I'm talking about?

Answer 13

yes

Answer 14

Okay so instead of (a+b)^3, we have (7x - 2y)^3. So now that you know that pattern, what will the terms be?

Answer 15

the first one is 7x^3

Answer 16

after tht I get stuck

Answer 17

alright so the next term you decrease the first terms exponent by 1, and then increase the second term's exponent by 1. So if you do that, what do you get?

Answer 18

-14x^2 (-2y^2) ?

Answer 19

Really close. If the first term is (7x)^3(-2y)^0, If you just do the step I said above, you end up with (7x)^2 (-2y)^1

Answer 20

You have to remember that the whole term gets the exponent applied to it.

Answer 21

so the third term is -2y^1?

Answer 22

The first term will be \[(7x)^{3}(-2y)^{0} \]
The second will be \[(7x)^{2}(-2y)^{1} \]
The third term will be \[(7x)^{1}(-2y)^{2} \]

If you simplify, you get\[ (7x)^{}(-2)^{2} y^{2} \]
Which is 7x 4y^2, multiply the 4 and 7 and you get 28.. so
28xy^2 (only the y has an exponent of 2)

Answer 23

Thank you

Answer 24

But then we have to find the coefficient of that term. and to do that we have to look at pascals triangle.



I don't know if that makes sense, but you count down to the 3rd row, and go to the 3rd term , and you get 3 as the coefficient.

So you multiply 3 by 28 and get 84xy^2.


I hope that makes sense.