# Math Help - EXPanD! yay

1. ## EXPanD! yay

(x+y)^4

My brain is going to explode

2. Could you show some work of what you've done so we know how we can help you?

3. Sure

I forgot how to use pascals triangle so I foiled two of the (x+y)

(x+y)(x+y) and got (x^2 +xy+xy+y^2)

now i need to multiply (x^2 +xy+xy+y^2)(x^2 +xy+xy+y^2)

I am stuck at that point

4. Ok well, we can do it your way first.
Just continue foiling you're almost there.
(x^2 + xy + xy+ y ^2) (x^2 + xy + xy+ y ^2)
You get
(x^2 + 2xy + y^2) (x^2 + 2xy + y^2)
Just finish it up.
(x^2)(x^2)+(x^2)(2xy)+(x^2)(y^2)..........
It's long, I know but if you forget pascal's triangle during a test, this is your best hope, write neatly and legibly.

As for Pascal's triangle...
You know that it's
1
11
121
1331
And so on...
If you think about it, these are the powers of 11.
11^0 = 1
11^1 = 11
11^2 = 121
.....
That's how I remember which level I take the numbers from.
Since you're expanding to 4.
You take it from the 4th level which is 1331
I recommend you write it out this way
1 * x * y
3 * x * y
3 * x * y
1 * x * y
Now you know from (x+y)^2, you get x^2 + 2xy + y^2
You would've gotten it this way.
1 * x^2 * y^0 = 1(x^2)(y^0) = x^2
2 * x^1 * y^1 = 2(x^1)(y^1) = 2xy
1 * x^0 * y^2 = 1(x^0)(y^2) = y^2
[Then you add them all up.
x^2 + 2 xy + y^2, that's the answer from (x+y)^2]
Realize how x starts from 2 and ends at 0 whereas y starts from 0 and ends at 2.
So does the same thing for this.
1 * x * y
3 * x * y
3 * x * y
1 * x * y
X starts from 4 and y starts from 0.
I hope this helps.

5. $(x+y)^4 = x^4 + 4x^3 y + 6x^2 y^2 + 4xy^3 + y^4$

Rapha

6. Originally Posted by Rapha
$(x+y)^4 = x^4 + 4x^3 y + 6x^2 y^2 + 4xy^3 + y^4$

Rapha
Giving just the final answer doesn't really help anyone...

If you know the Binomial Theorem, then you should know that

$(a + b)^n = \sum_{r = 0}^{n}{\left(^n_r\right)a^{n - r}b^r}$.

So in this case, $a = x, b = y, n = 4$.

So you have $(x + y)^4 = \sum_{r = 0}^{4}{\left(^4_r\right)x^{4 - r}y^r}$

$= \left(^4_0\right)x^4y^0 + \left(^4_1\right)x^3y^1 + \left(^4_2\right)x^2y^2 + \left(^4_3\right)x^1y^3 + \left(^4_4\right)x^0y^4$

$= x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4$.

7. Hello Prove it!

Originally Posted by Prove It
Giving just the final answer doesn't really help anyone...
Did you read Winglessarch's explanation? In my opinion it is a good answer, but the solution was missing. So I only posted the final answer.

8. Originally Posted by Rapha
Hello Prove it!

Did you read Winglessarch's explanation? In my opinion it is a good answer, but the solution was missing. So I only posted the final answer.
Fair enough - if you're going to do that though please write something like "And so from the above post, we can see the answer is ..."

Then an OP is not as likely to just skim over the working out and just go straight to the answer.