How would you use the binomial theorem to expand and simplify (2x^2 - 4x + 7)^3.
I haven't done a question like this before.. I need helpp thankss

This is a trinomial expansion.

Using a Pascal-type triangle.


\;\ \;\ \;\ \;\ \;\ \;\ x^{3} \;\ \;\ \;\ \;\

\;\ \;\ \;\ 3x^{2}y \;\ \;\ \;\ 3x^{2}z

\;\ 3xy^{2} \;\ \;\ \;6xyz \;\ \;\ \;\ \;\ 3xz^{2}

y^{3} \;\ \;\ 3y^{2}z \;\ \;\ \;\ 3yz^{2} \;\ \;\ \;\ \;\ z^{3}

Just enter your values for x,y, and z.

There are some cool properties of the trinomial:

Reading down the left we have (x+y)^{3}

Reading down the right edge we have (x+z)^{3}

Reading across the bottom we have (y+z)^{3}

If we stack these up, we have Pascal's tetrahedron.

Every number is the sum of the 3 numbers above it.


i.e. At the top we have x^{3}. Plug in 2x^{2} and get

(2x^{2})^{3}=8x^{6}

That is the first term starting at the left.

The next term would be at the 3x^{2}y

Sub in 2x^{2} for x and -4x for the y.

We get -48x^{5}. That is the next term in the expansion. Continue.