could someone help me im super stressed about this/

Question

Factor the polynomial completely.

 

48a⁵b²−24a⁴b³+3a³b⁴

 

Answer 1

Hi!

That's one hefty problem!

First lets pull that 3 out of there since it is a factor of 3, 24, and 28.

Now we have 3(16a⁵b² - 8a⁴b^3 + a³b⁴)

 

Now lets look at A. a³ is the smallest A we have so lets pull that out too! 

Now we have 3a³(16a²b² - 8ab³ + b⁴)

 

Were getting close! There's only one more variable left that looks like it repeats and that's B! Looks like b² can be pulled out as well so lets do that!

Now we have 3a³b²(16a²-8ab + b²)

 

It almost looks like were done considering we've factored out a 3, an a³, and a b² but there's one more thing we can do. notice that what's inside the parenthesis is a quadratic. That means there's a chance that we can factor that too!

 

Lets do it.

 

(4a - b)(4a - b)

 

Lets double check to make sure it works. To do that we foil it. 

4a * 4a= 16a²

4a * -b= -4ab

-b * 4a= -4ab

-b * -b= b²

 

adding those up we get 16a²-8ab+b²

 

Looks like it worked so were finally done!

 

Our answer is 

                              3a³b²(4a-b)²

 

Best of Luck! 

Answer 2

3a^3b^2(4a-b)^2

Answer 3

Hi Jared,

 

You need to find the largest things that each term has in common and factor them out. .

 

You can divide all the terms by 3, a^3, and b^2.  Remember that you add exponents when you multiply terms with exponents.

 

So--> 3(a^3)(b^2) (16a^2 - 8ab + b^2)

 

Dan