Can someone tell me how to factor
2a^2 - 16ab + 32b
I just need someone to help me get started, and I want to see if I can finish it.
Pull a 2 out first...
2(a^2 - 8ab + 32b^2)
That should get you started
2a^2 - 16ab + 32b = 2(a^2 - 8ab + 16b^2) = 2(a^2 + 8(2b - ab))
(DanH made a mistake: The 32 should be a 16 since a 2 was factored from it)
Ohh I'm sorry, The problem was
2a^2b -16ab+32b
So should it be
So should I factor with 2b?
You only factor out what all of the terms share.
Not all of the terms share 2b as a factor (only the -16ab and +32b terms can have a 2b factored from them. The 2b in the 2a^2b term is in the exponent, which can't be used as a factor.)
So what do all 3 terms share? That's what you factor.
well they all share 2 like you said so
2(a^2b - 8ab + 16b)
that makes it the perfect square trinomial
But I have no idea how to factor that. If that b was gone from the a^2b, than I can do it, but with the b there, i have no clue.
Sure, I can help you get started with factoring the expression.
To factor the given expression 2a^2 - 16ab + 32b, we first look for any common factors among the three terms. In this case, we can see that each term has a common factor of 2. So, we can factor out the greatest common factor, which is 2:
2(a^2 - 8ab + 16b)
Now, we need to factor the trinomial inside the parentheses, which is a^2 - 8ab + 16b.
To factor a quadratic trinomial, we look for two binomials whose product gives us the trinomial.
In this case, a^2 - 8ab + 16b can be factored as (a - 4b)(a - 4b) or (a - 4b)^2.
Therefore, the fully factored expression is:
2(a - 4b)^2
Now, you can try to solve it on your own.