Simplify the Expression: a(a+b)-ab(5a-6b) Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Distribute the first part of the expression $a(a+b)$.
• Step 2: Distribute the second part of the expression $-ab(5a-6b)$.
• Step 3: Combine the expressions obtained from steps 1 and 2.
• Step 4: Combine like terms.

Now, let's work through each step:

Step 1: Distribute $a(a+b)$:
$a(a+b) = a \cdot a + a \cdot b = a^2 + ab$.

Step 2: Distribute $-ab(5a-6b)$:
$-ab(5a-6b) = -ab \cdot 5a + (-ab) \cdot (-6b) = -5a^2b + 6ab^2$.

Step 3: Combine the results obtained from these two distributions:
$(a^2 + ab) + (-5a^2b + 6ab^2)$.

Step 4: Combine like terms:
The expression is already simplified as all terms are unique.
Therefore, the simplified form of the expression is $a^2 + ab - 5a^2b + 6ab^2$.

Therefore, the solution to the problem is $a^2 + ab - 5a^2b + 6ab^2$.