Simplify the Expression: 4a(a-b)+3b(a-b) Using Factoring

To solve this problem, we'll expand and simplify the given expression $4a(a-b) + 3b(a-b)$ by applying the distributive property.

Let's go through the steps:

• Step 1: Apply the distributive property to the first term.
  $4a(a-b) = 4a \cdot a - 4a \cdot b = 4a^2 - 4ab$
• Step 2: Apply the distributive property to the second term.
  $3b(a-b) = 3b \cdot a - 3b \cdot b = 3ab - 3b^2$
• Step 3: Combine the results from Step 1 and Step 2.
  Combine like terms: $4a^2 - 4ab + 3ab - 3b^2 = 4a^2 - ab - 3b^2$

Therefore, the simplified form of the expression is $4a^2 - ab - 3b^2$.

Among the given choices, the correct answer is:

$4a^2-ab-3b^2$