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!!
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 $\displaystyle \left(\begin{pmatrix}4 \\ 2\end{pmatrix}(3)(-2)^2+ \begin{pmatrix}4 \\ 3\end{pmatrix}(4)(-2)\right)x^3$