Expanding a Cube

[Jason76]

\(\displaystyle (x^{2} + 2x - 1)^{3}\)

What is the first step?

 

[mmm4444bot]

Square it first?

Or, is this your way of beginning some discussion about the binomial theorem...

 

[Jason76]

Square it first?

Or, is this your way of beginning some discussion about the binomial theorem...

\(\displaystyle (x^2 + 2x - 1)^{2}\)

\(\displaystyle (x^2 + 2x - 1)(x^2 + 2x - 1)\) ???

 

[mmm4444bot]

\(\displaystyle (x^2 + 2x - 1)(x^2 + 2x - 1)\)

Yes -- now use the Distributive Property.

Each term in the second factor gets multiplied by each term in the first factor.

Symbolic example:

(a + b + c)(x + y + z) =

ax + ay + az + bx + by + bz + cx + cy + cz

 

[Jason76]

Yes -- now use the Distributive Property.

Each term in the second factor gets multiplied by each term in the first factor.

Symbolic example:

(a + b + c)(x + y + z) =

ax + ay + az + bx + by + bz + cx + cy + cz

\(\displaystyle (x^2 + 2x - 1)^{3}\)


\(\displaystyle (x^2 + 2x - 1)^{2}\)

\(\displaystyle (x^2 + 2x - 1)(x^2 + 2x - 1)\)

\(\displaystyle x^{2}(x^{2}) + x^{2}(2x) + x^{2}(-1) + 2x(x^{2}) + 2x(2x) + 2x(-1) + -1(x^{2}) + -1(2x) + -1(-1) \)

\(\displaystyle x^{4} + 2x^{3} - x^{2} + 2x^{3} + 4x^{2} - 2x - x^{2} - 2x + 1\)

This can be simplified further somehow. ? What about the cube?

 

[Deleted member 4993]

\(\displaystyle (x^2 + 2x - 1)^{3}\)


\(\displaystyle (x^2 + 2x - 1)^{2}\)

\(\displaystyle (x^2 + 2x - 1)(x^2 + 2x - 1)\)

\(\displaystyle x^{2}(x^{2}) + x^{2}(2x) + x^{2}(-1) + 2x(x^{2}) + 2x(2x) + 2x(-1) + -1(x^{2}) + -1(2x) + -1(-1) \)

\(\displaystyle x^{4} + 2x^{3} - x^{2} + 2x^{3} + 4x^{2} - 2x - x^{2} - 2x + 1\)

This can be simplified further somehow. ? What about the cube?

x^{4} + 2x^{3} - x^{2} + 2x^{3} + 4x^{2} - 2x - x^{2} - 2x + 1

Now collect the terms with "same power of x" - and simplify.

For cube - multiply the whole thing again (after simplification) by (x² + 2x - 1) and collect similar terms and simplify.

 

[mmm4444bot]

\(\displaystyle x^{4} + 2x^{3} - x^{2} + 2x^{3} + 4x^{2} - 2x - x^{2} - 2x + 1\)

This can be simplified further somehow. ?

I understand that you do not like studying math, but you could save yourself a lot of time by considering some very basic lessons.

The expression -x^2 - x^2 simplifies to -2x^2.

We call this process "combining like-terms".

The method of combining like-terms is described within tens of thousands of lessons on the Internet -- like this one!

Could you force yourself to study an introductory lesson, just this once? :cool: