Help with an algebra factoring problem.

[gohabsgo]

Sorry to ask help on such an easy problem. I'm self teaching, but for some reason I'm getting stuck on a step. Can anyone explain to me what to do once I reach the form below, prior to the answer?

1) 15(x-3)³ + 60x⁴(x-3)² + 5(x-3)




I get this far, as shown below. After this I'm confused as to what to do next. For instance, (x-3)^2, could be x^2-9, allowing me to use difference of squares, but I'm at a loss when I look at the answer my book gives. Somewhere I'm forgetting something. As for 12x^4, I understand that it's been distributed to give the 12x^5-36x^4, but after that I'm completely lost.
3) 5(x-3) [3(x-3)² + 12x⁴(x-3) +1]

According to my material the Answer is: 5(x-3)[12x⁵ - 36x⁴ +3x² -18x +28]

 

[elabed haidar]

just expand the second part and you are okay

 

[Mark44]

Sorry to ask help on such an easy problem. I'm self teaching, but for some reason I'm getting stuck on a step. Can anyone explain to me what to do once I reach the form below, prior to the answer?

1) 15(x-3)³ + 60x⁴(x-3)² + 5(x-3)




I get this far, as shown below. After this I'm confused as to what to do next. For instance, (x-3)^2, could be x^2-9, allowing me to use difference of squares

No, (x - 3)² = x² - 6x + 9, which is different from x² - 9.

, but I'm at a loss when I look at the answer my book gives. Somewhere I'm forgetting something. As for 12x^4, I understand that it's been distributed to give the 12x^5-36x^4, but after that I'm completely lost.

Factor 5(x - 3) from each of the three terms above, to get what you have just below here. Then expand everything inside the brackets and combine like terms.

3) 5(x-3) [3(x-3)² + 12x⁴(x-3) +1]

According to my material the Answer is: 5(x-3)[12x⁵ - 36x⁴ +3x² -18x +28]

 

[gohabsgo]

No, (x - 3)² = x² - 6x + 9, which is different from x² - 9.
Factor 5(x - 3) from each of the three terms above, to get what you have just below here. Then expand everything inside the brackets and combine like terms.

Oh wow Mark44, thanks. So all I had to do was distribute 3 through (x² -6x +9) and combine like-terms? I think where I became confused was with the lone 3. I didn't think to keep x² -6x +9 in brackets to thereafter distribute 3. It's all so clear now and makes perfect sense. Thanks again for the help on something I was literally going crazy over. :)