Paul's Online Notes
Home / Algebra / Preliminaries / Polynomials
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 1.4 : Polynomials

8. Perform the indicated operation and identify the degree of the result.

$3{\left( {10 - 4{y^3}} \right)^2}$

Show All Steps Hide All Steps

Start Solution

Remember that this is just another way of writing,

$3{\left( {10 - 4{y^3}} \right)^2} = 3\left( {10 - 4{y^3}} \right)\left( {10 - 4{y^3}} \right)$

Now all we need to do is foil out the two polynomials. Here is the result of doing that.

$3{\left( {10 - 4{y^3}} \right)^2} = 3\left( {10 - 4{y^3}} \right)\left( {10 - 4{y^3}} \right) = 3\left( {100 - 80{y^3} + 16{y^6}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{300 - 240{y^3} + 48{y^6}}}$

Be careful with dealing with the three! Make sure you take care of the exponent first (i.e. make sure you multiply out the product first) before you multiply the three through the result.

Show Step 2

Remember the degree of a polynomial is just the largest exponent in the polynomial and so the degree of the result of this operation is six.