Help me with the multiplication of polynomials

[lenkskendi]

Could you help me with this polynomial multiplication exercise?

$\qquad \left(\frac{3}{2}\,x^5 + 0x^4 + 0x^3 + 5x^2 - \frac{2}{3}\,x-15\right)\cdot\left(2x^3 + \frac{4}{5}\,x^2\right)$

 

[stapel]

Could you help me with this polynomial multiplication exercise?

$\qquad \left(\frac{3}{2}\,x^5 + 0x^4 + 0x^3 + 5x^2 - \frac{2}{3}\,x-15\right)\cdot\left(2x^3 + \frac{4}{5}\,x^2\right)$

We'd be glad to help!

But first, we need to be able to see where you're stuck. Kindly please reply with the information outlined in the "Read Before Posting" message, so we can understand where you're having difficulty.

For instance, you set up the vertical multiplication as so:

$$\begin{array}{r} \frac{3}{2}\,x^5 + 0x^4 + 0x^3 + 5x^2 - \frac{2}{3}\,x-15 \\[1em] \underline{\phantom{\frac{3}{2}\,x^5 + 0x^4 + 0x^3 + 5x^2} 2x^3 + \frac{4}{5}\,x^2} \end{array}$$
What did you do next? And so forth.

Thank you!

Eliz.

 

[lookagain]

$\qquad \left(\frac{3}{2}\,x^5 + 0^4 + 0^3 + 5x^2 - \frac{2}{3}\,x-15\right)\cdot\left(2x^3 + \frac{4}{5}\,x^2\right)$
View attachment 35833

The zeros are the coefficients of the x-terms, so the exponents need to be shown operating on the variables.
Also, the multiplication dot is optional.

$\displaystyle \bigg(\dfrac{3}{2}x^5 \ + \ 0x^4 \ + \ 0x^3 \ + \ 5x^2 \ - \ \dfrac{2}{3}x \ - \ 15\bigg)\bigg(2x^3 \ + \ \dfrac{4}{5}x^2\bigg)$

 

[stapel]

The zeros are the coefficients of the x-terms, so the exponents need to be shown operating on the variables.
Also, the multiplication dot is optional.

$\displaystyle \bigg(\dfrac{3}{2}x^5 \ + \ 0x^4 \ + \ 0x^3 \ + \ 5x^2 \ - \ \dfrac{2}{3}x \ - \ 15\bigg)\bigg(2x^3 \ + \ \dfrac{4}{5}x^2\bigg)$

I've made the corrections. Thank you!