What is the standard form of # y= (-7x-9)^3-(2x-1)^2#?

1 Answer
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Nov 24, 2017

#y=-343x^3-1327x^2-1697x-730#

Explanation:

This is a really ugly problem, but the binomial theorem helps a lot. The binomial theorem lets you raise binomials to high powers without exhausting a lot of time.

We'll tackle the cube first.

#(x+y)^n=sum_(r=0)^n""^nC_rx^(n-r)y^r#

Here, we can substitute our values.

#(-7x+ -9)^3=sum_(r=0)^3""^3C_r(-7x)^(3-r)(-9)^r#

Using the binomial theorem, we can find that:

#(-7x-9)^3=-343x^3+3*49x^2*-9+3*-7x*81+ -729#

#(-7x-9)^3=-343x^3-1323x^2-1701x-729#

The second part is easier:

#-(2x-1)^2=-(4x^2-4x+1)=-4x^2+4x-1#

Now we add the two together:

#y=-343x^3-1327x^2-1697x-730#

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