Calculate Rectangle Area: Finding (x-7)(x+8) Using Algebraic Expressions

To tackle this problem, we must compute the area of a rectangle given its sides are expressed as $x-7$ and $x+8$.

Step 1: Start by recognizing the formula used to calculate the area of a rectangle: the product of its length and width.

Step 2: Substitute the given expressions for length and width into this formula:

$\text{Area} = (x-7)(x+8)$

Step 3: Multiply the binomial expressions using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).

• First terms: $x \times x = x^2$
• Outer terms: $x \times 8 = 8x$
• Inner terms: $-7 \times x = -7x$
• Last terms: $-7 \times 8 = -56$

Step 4: Combine all these products into a single polynomial expression:

$x^2 + 8x - 7x - 56$

Step 5: Simplify by combining like terms:

$x^2 + (8x - 7x) - 56 = x^2 + x - 56$

Therefore, the area of the rectangle is given by the polynomial expression: $x^2 + x - 56$.