Can someone tell me how to factor
2a^2b - 16ab + 32b
Should I factor 2b out of it?
I answered this question in your last post.
yes, which give you
2b(a^2 - 8a + 16)
= 2b(a-4)^2
Who wait, but i thought you cant factor using b because ab is a term by itself
If the b is not part of the exponent, my last response was incorrect.
Well if your talking about the 2a^2b its 2a^2 * b the exponent is only with the a. So does that mean 2b can factor?
To factor the given expression, you can use the process of factoring by grouping.
First, let's rearrange the expression:
2a^2b - 16ab + 32b
Next, look for any common factors.
In this case, there is a common factor of 2b in each term, so you can factor it out:
2b(a^2 - 8a + 16)
Now, we can focus on what remains inside the parentheses: (a^2 - 8a + 16)
To further factor this quadratic expression, let's find two numbers that multiply to give the constant term (16) and add up to the coefficient of the middle term (-8).
In this case, the numbers are -4 and -4:
(-4) * (-4) = 16
(-4) + (-4) = -8
So, we can rewrite the quadratic as:
a^2 - 8a + 16 = (a - 4)(a - 4)
Therefore, the fully factored expression is:
2b(a - 4)(a - 4)
So, yes, you should factor 2b out of the original expression to simplify it.