[Fan + Medal]

Use Pascal's triangle to expand the binomial.
(d - 5y)^6

Question

[Fan + Medal]

Use Pascal's triangle to expand the binomial.
(d - 5y)^6

abdullahm · Answer

https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcR-HwePauqkqm86-NMuW1BN1gSMTXwgmAqqTkvrcU7rLvnK7byB We want to use the numbers in Row 6

abdullahm · Answer

An example:

(x + y)^4

We would use the numbers in row 4, and would get:

$\bf\Large x^4+4x^3y+6x^2y^2+4xy^3+y^4$

ltrout · Answer

I see how to do it when the coefficients are 1, but not when they are greater than 1.

abdullahm · Answer

ok, if we had (x - y)^6, what would we get when we expand it?

ltrout · Answer

$$x ^{6} - 6x ^{5}y + 15x^{4}y^{2}-20x^{3}y^{3}+15x^{2}y{4}-6xy^{5}-y^{6}$$?

ltrout · Answer

Wait no, the final part would be + y^6*

abdullahm · Answer

Good job.

Now, the question gave us:

(d - 5y)^6

Now, you replace the x with d, and the y with 5y.

So we now get:

$$\bf d ^{6} - 6d ^{5}(5y) + 15d^{4}(5y)^{2}-20d^{3}(5y)^{3}+15d^{2}(5y)^{4}-6d(5y)^{5}+(5y)^{6}$$

All you have to do to get the final answer is find out what 5^1, 5^2, and so on are and multiply that with the coefficient in front of it.

abdullahm · Answer

Do you understand?

ltrout · Answer

Okay that's what I thought. Thanks! :)

dani_rose · Answer

attachment

dani_rose · Answer

Hopefully that explains your problem