y^2 - xy - 56x^2 Factor completely
In order to factor the expression completely, we need to find two binomials that multiply together to give the original expression.
To start, we can look for common factors in the original expression:
y^2 - xy - 56x^2
The greatest common factor is 1, so there are no common factors to pull out.
Next, we need to look for a trinomial that multiplies together to give the original expression.
We need to find two numbers that multiply to give -56 and add to give -1 (from the -xy term).
The numbers that satisfy these conditions are -8 and 7.
So, we can rewrite the original expression as:
y^2 - xy - 56x^2 = y^2 -8xy + 7xy - 56x^2
Now, we can group the terms:
= (y^2 - 8xy) + (7xy - 56x^2)
Next, we factor out the greatest common factor from each group:
= y(y - 8x) + 7x(y - 8x)
Now we can see that we have a common factor of (y - 8x), so we can factor that out:
= (y - 8x)(y + 7x)
Therefore, the expression y^2 - xy - 56x^2 completely factors to (y - 8x)(y + 7x).