Factor completely. Be sure to factor out the GCF when necessary.
Select "Prime" if the polynomial cannot be factored.
\[
x^{2}+2 x y-8 y^{2}
\]
\[
x^{2}+2 x y-8 y^{2}=\square
\]
Prime
Answer
\(\boxed{x^{2}+2 x y-8 y^{2}=(x - 2y)(x + 4y)}\)
Step 1 ：The given expression is a quadratic expression in the form of \(ax^2 + bx + c\). To factorize it, we need to find two numbers such that their sum is equal to the coefficient of the middle term (which is 2 in this case) and their product is equal to the product of the coefficients of the first and last terms (which is -8 in this case).
Step 2 ：By inspection, we can see that the two numbers that satisfy these conditions are -2 and 4. Therefore, we can write the given expression as \((x - 2y)(x + 4y)\).
Step 3 ：\(\boxed{x^{2}+2 x y-8 y^{2}=(x - 2y)(x + 4y)}\)
