If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?

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Question: If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?

Options:

Correct Answer: x^2 - x - 6

Solution:

Area = Length × Width = (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6.

If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?

If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?

Step 1: Identify the formula for the area of a rectangle, which is Area = Length × Width.
Step 2: Substitute the given length (x + 2) and width (x - 3) into the formula: Area = (x + 2)(x - 3).
Step 3: Use the distributive property (also known as FOIL) to multiply the two binomials: (x + 2)(x - 3).
Step 4: Multiply the first terms: x × x = x^2.
Step 5: Multiply the outer terms: x × -3 = -3x.
Step 6: Multiply the inner terms: 2 × x = 2x.
Step 7: Multiply the last terms: 2 × -3 = -6.
Step 8: Combine all the results from steps 4 to 7: x^2 - 3x + 2x - 6.
Step 9: Combine like terms (-3x and 2x): x^2 - x - 6.
Step 10: Write the final expression for the area: Area = x^2 - x - 6.

Area of a Rectangle – The area of a rectangle is calculated by multiplying its length by its width.
Algebraic Expansion – The question tests the ability to expand a binomial expression correctly.