1. ## [SOLVED] Expanding Bionomial

I am trying to expand the Binomial (x - 4y)5 .

this is what I got , can someone tell me , where I went wrong or correct me.

X^5-(4^0*y^0)+x^4(4^1*y^1)+X^3-(4^2*y^2)+x^2-(4^3*y^3)+x-(4^4*y^4)+x^0-(4^5*y^5)
(x^5-1)+(x^4-4y)+(x^3-16y^2)+(x^2-64y^3)+(x-256y^4)+(1025y^5)

Thanks , AC

2. It should be:

$\displaystyle x^5-20x^4y+160x^3y^2-640x^2y^3+1280xy^4-1024y^5$

3. Hello, AlgebraicallyChallenged!

Better review the Binomial Expansion . . .

You totally forgot the Binomial Coefficients,
. . and you're writing those minus-signs incorrectly.

Expand: .$\displaystyle (x - 4y)^5$

This is what you should have had . . .

x^5(-4y)^0 + 5x^4(-4y)^1 + 10x^3(-4y)^2 + 10x^2(-4y)^3 + 5x(-4y)^4 + x^0(-4y)^5

The expansion is: .$\displaystyle (a - b)^5 \;=\;a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5$

We have: .$\displaystyle x^5 - (5)(x^4)(4y) + (10)(x^3)(4y)^2 - 10(x^2)(4y)^3 + (5)(x)(4y)^4 - (4y)^5$

. . . . . . $\displaystyle = \;x^5 - (5x^4)(4y) + (10x^3)(16y^2) - (10x^2)(64y^3) + (5x)(256y^4) - 1024y^5$

. . . . . . $\displaystyle = \;x^5 - 20x^4y + 160x^3y^2 - 640x^2y^3 + 1280xy^4 - 1024y^5$

. . . . . as Amanda promised.

### bionomial expansion of (1 x y)^3

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