(x + 2y)^2 simplified
i need to know how to do this..
(x+2y)^2
= (x+2y)(x+2y)
= x^2 + 2xy + 2xy + 4y^2
= x^2 + 4xy + 4y^2
The method I used is sometimes referred to a FOIL
To simplify the expression (x + 2y)^2, we can expand the expression and combine like terms. Here's how you can do it:
Step 1: Square the binomial (x + 2y) using the FOIL method.
(x + 2y)^2 = (x + 2y) * (x + 2y) = x * x + x * 2y + 2y * x + 2y * 2y
Step 2: Simplify each term.
x * x = x^2
x * 2y = 2xy (since x * y = xy)
2y * x = 2xy (since y * x = yx = xy)
2y * 2y = 4y^2
Step 3: Combine the like terms.
x^2 + 2xy + 2xy + 4y^2 = x^2 + 4xy + 4y^2
So, the simplified form of (x + 2y)^2 is x^2 + 4xy + 4y^2.