# What is the standard form of #y-4x= -(x-1)^2(x-1)^3#?

##### 1 Answer

May 15, 2016

#### Explanation:

Notice that

The binomial theorem tells us that:

#(a+b)^n = sum_(k=0)^n ((n),(k)) a^(n-k)b^k#

where the binomial coefficient:

The binomial coefficients can be found as rows in Pascal's triangle:

The row

#(a+b)^5 = a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5#

Then put

#(x-1)^5 = x^5-5x^4+10x^3-10x^2+5x-1#

So:

#y - 4x#

#= -(x-1)^2(x-1)^3#

#= -(x-1)^5#

#= -(x^5-5x^4+10x^3-10x^2+5x-1)#

#= -x^5+5x^4-10x^3+10x^2-5x+1#

Add

#y = -x^5+5x^4-10x^3+10x^2-x+1#

This has the powers of