solve by factoring a^2-4ab-8b^2?
No factors over the integers. But, you do have
(a-2b)^2 - 12b^2
as a difference of two squares, that'd be
(a-2b + √12 b)(a-2b - √12 b)
or
(a-2(1-√3)b)(a-2(1+√3)b)
To solve the expression "a^2 - 4ab - 8b^2" by factoring, we need to find two binomials whose product will result in the given expression.
First, let's focus on the coefficient of the quadratic term, which is "1" (since the coefficient is always 1 when the term is written as a^2).
Next, we need to find two numbers whose product is the product of the coefficient of the quadratic term (1) and the constant term (-8b^2), which gives us -8. These numbers should also add up to the coefficient of the linear term (-4ab).
To find these numbers, we can factor -8 into two numbers that satisfy the above conditions. The factors of -8 are: (-1, 8), (1, -8), (-2, 4), and (2, -4).
Among these factors, we can see that (-2, 4) satisfies both conditions.
Now, we can rewrite the expression as follows by splitting the middle term (-4ab) using the factors found:
a^2 - 2ab - 2ab - 8b^2
Notice that the common factor "-2b" can be extracted from the first two terms and the last two terms:
a(a - 2b) - 2b(a - 2b)
Now, we have a common binomial factor of (a - 2b) that can be factored out:
(a - 2b)(a - 2b)
We can rewrite this as:
(a - 2b)^2
So, the factored form of the expression "a^2 - 4ab - 8b^2" is "(a - 2b)^2".