y^2+13y+40
using the foil method, explain your work
To factor the quadratic expression y^2 + 13y + 40 using the FOIL (First, Outer, Inner, Last) method, we first need to find two numbers that multiply to 40 (the product of the first and last coefficients) and add up to 13 (the middle coefficient).
The two numbers that satisfy these criteria are 5 and 8 (5*8 = 40 and 5 + 8 = 13).
Now, we rewrite the middle term of the expression (13y) using these two numbers:
y^2 + 5y + 8y + 40
Next, we group the terms and factor out the common factors:
y(y + 5) + 8(y + 5)
Finally, we factor out the common binomial factor:
(y + 5)(y + 8)
Therefore, the factored form of the expression y^2 + 13y + 40 is (y + 5)(y + 8).