how can i do this right?

Question

Factor the polynomial completely.

3a² +6ab+3b²

Answer 1

3a² +6ab + 3b²

First we can factor out a 3:

3(a² + 2ab + b²)

Now to factor this polynomial we need:

n + m = b (in this case b is the coefficient in front of the middle term)

n * m = c (c is the coefficient in front of the third term)

1 + 1 = 2

1 * 1 = 1

3(a + b)(a + b) (you can FOIL that out to see it's correct)

Simplify:

3(a + b)²

Answer 2

Here’s what you’re starting with: 3a² + 6ab + 3b² First, find the greatest common factor. In this case, it’s 3. 3(a² + 2ab + b²) Next, you may notice that the part in the parentheses can also be factored: (a² + 2ab + b²) = (a + b)(a + b) (a + b)(a + b) can also be written as (a + b)² There’s nothing else you can factor after that, so you’re done: 3(a + b)²

Answer 3

Hi Jared,

 

    Factor the polynomial completely.
      3a² +6ab+3b²

 

Factor out the GCF=3

 

                 3(a²+2ab+b²)

Then factor the quadratic:

 

                 3(a +b)(a +b)           It can also be written as  3(a + b)²