Calculate Rectangle Area: Finding Area When Length is (8a-b) and Width is (2a+3b)

To solve this problem, we need to calculate the area of the rectangle with side lengths $(8a-b)$ and $(2a+3b)$.

The area $A$ is found by multiplying these two expressions:

• Step 1: Write the expression for the area:
  $A = (8a-b)(2a+3b)$
• Step 2: Use the distributive property to expand the product:
  $A = 8a(2a) + 8a(3b) - b(2a) - b(3b)$.
• Step 3: Calculate each term individually:
  - $8a \times 2a = 16a^2$
  - $8a \times 3b = 24ab$
  - $-b \times 2a = -2ab$
  - $-b \times 3b = -3b^2$
• Step 4: Combine like terms:
  $A = 16a^2 + 24ab - 2ab - 3b^2$, which simplifies to $16a^2 + 22ab - 3b^2$.

Therefore, the area of the rectangle, expressed in terms of $a$ and $b$, is $16a^2 + 22ab - 3b^2$.