Which expression is the product of (x + 3)(x + 2) after applying FOIL?

Which expression is the product of (x + 3)(x + 2) after applying FOIL?

• A. x^2 + 7x + 6
• B. x^2 + 5x + 7
• C. x^2 + 5x + 6
• D. x^2 + 6x + 5

Answer: (C)

Expanding with FOIL means multiply the First terms, the Outer and Inner cross terms, and the Last terms, then combine like terms. For (x + 3)(x + 2): - First: x * x = x^2 - Outer: x * 2 = 2x - Inner: 3 * x = 3x - Last: 3 * 2 = 6 Add them up: x^2 + 2x + 3x + 6 = x^2 + 5x + 6. So the product is x^2 + 5x + 6. This matches the expression that has the correct middle term 5x and the constant 6. The other options misstate either the middle term or the constant.

Expanding with FOIL means multiply the First terms, the Outer and Inner cross terms, and the Last terms, then combine like terms. For (x + 3)(x + 2):

• First: x * x = x^2

• Outer: x * 2 = 2x

• Inner: 3 * x = 3x

• Last: 3 * 2 = 6

Add them up: x^2 + 2x + 3x + 6 = x^2 + 5x + 6.

So the product is x^2 + 5x + 6. This matches the expression that has the correct middle term 5x and the constant 6. The other options misstate either the middle term or the constant.