Expanding (x+4)(x+9)
The expression (x+4)(x+9) represents the product of two binomials. To find the answer, we need to expand this expression using the distributive property or the FOIL method.
Using the Distributive Property
The distributive property states that a(b+c) = ab + ac. We can apply this property twice to expand our expression:

Distribute (x+4) over (x+9): (x+4)(x+9) = (x+4)*x + (x+4)*9

Distribute x and 9: (x+4)x + (x+4)9 = xx + 4x + 9x + 49

Simplify: xx + 4x + 9x + 49 = x² + 13x + 36
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us remember to multiply all the terms correctly:

Multiply the First terms: x * x = x²

Multiply the Outer terms: x * 9 = 9x

Multiply the Inner terms: 4 * x = 4x

Multiply the Last terms: 4 * 9 = 36

Combine the terms: x² + 9x + 4x + 36 = x² + 13x + 36
The Answer
Therefore, the expanded form of (x+4)(x+9) is x² + 13x + 36. This is a quadratic expression, meaning it has a highest power of 2 for the variable x.