Evaluate : (iii) `(4a - 3b) (2a + 5b)`

Answer

To evaluate the expression \((4a - 3b)(2a + 5b)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute the first term of the first binomial
Multiply \(4a\) by each term in the second binomial \((2a + 5b)\):
\[ 4a \cdot 2a = 8a^2 \]
\[ 4a \cdot 5b = 20ab \]

### Step 2: Distribute the second term of the first binomial
Now, multiply \(-3b\) by each term in the second binomial \((2a + 5b)\):
\[ -3b \cdot 2a = -6ab \]
\[ -3b \cdot 5b = -15b^2 \]

### Step 3: Combine all the results
Now, we combine all the terms we calculated:
\[ 8a^2 + 20ab - 6ab - 15b^2 \]

### Step 4: Combine like terms
Combine the \(ab\) terms:
\[ 20ab - 6ab = 14ab \]
So, the expression simplifies to:
\[ 8a^2 + 14ab - 15b^2 \]

### Final Answer
The evaluated expression is:
\[ 8a^2 + 14ab - 15b^2 \]

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