Thread: Binomial Expansions, what is the term

1. Binomial Expansions, what is the term

Hello!
This is the question,
find the term x^3 in

Code:
(3x +4 ) (x − 2)^4

I dont know how to start or what is ment by the 'term',

do i expand (x − 2)^4?

Thank you!!

2. Originally Posted by appleseed
Hello!
This is the question,
find the term x^3 in

Code:
(3x +4 ) (x − 2)^4
I dont know how to start or what is ment by the 'term',

do i expand (x − 2)^4?

Thank you!!
Expand (x-2)^4and multiply it with (3x+4) and collect the terms containing x^3.

3. Originally Posted by appleseed
Hello!
This is the question,
find the term x^3 in

Code:
(3x +4 ) (x − 2)^4

I dont know how to start or what is ment by the 'term',

do i expand (x − 2)^4?

Thank you!!
hi

yes you expand but not everything ,

(3x+4)(x-2)^4=(3x+4)(x^4+4(-2)x^3+6(-2)^2x^2+...)

=(6x^2)(4)(3x)+(4)(-2)(4x^3)

notice that you can ignore those terms which will not generate x^3 when multiplied .

4. Thank you guys! this really helps

5. Since you titled this "binomial expansions", presumably you know the "binomial coefficients" and using those you don't need to do all that work.

You can get $\displaystyle x^3$ by multiplying that "3x" by the $\displaystyle x^2$ term in the fourth power expansion and by multiplying "4" by the $\displaystyle x^3$ term.

The $\displaystyle x^2$ term in $\displaystyle (x- 2)^4$ is $\displaystyle \begin{pmatrix}4 \\ 2\end{pmatrix}(-2)^2x^2$ and the $\displaystyle x^3$ term is $\displaystyle \begin{pmatrix}4 \\ 3\end{pmatrix}(-2)^1x^3$.

Multiplying the first by 3x and the second by 4 gives $\displaystyle \left(\begin{pmatrix}4 \\ 2\end{pmatrix}(3)(-2)^2+ \begin{pmatrix}4 \\ 3\end{pmatrix}(4)(-2)\right)x^3$