Question

\\(a-b)(c-d)\\

Explanation:

🆕 New Concept Discovered: FOIL Method
Multiply binomials by distributing every term.

Step 1: Understand the expression

The image shows the multiplication of two binomials:

$$ (a - b)(c - d) $$

To expand this, we need to multiply each term in the first parentheses by each term in the second parentheses. A helpful way to remember this is the FOIL method:

• First: Multiply the first terms in each set of parentheses.
• Outer: Multiply the outermost terms.
• Inner: Multiply the innermost terms.
• Last: Multiply the last terms in each set of parentheses.

Step 2: Apply the FOIL method

Let's multiply the terms step-by-step, keeping careful track of the positive and negative signs:

1. First: Multiply \( a \) and \( c \)

$$ a \cdot c = ac $$

1. Outer: Multiply \( a \) and \( -d \)

$$ a \cdot (-d) = -ad $$

1. Inner: Multiply \( -b \) and \( c \)

$$ -b \cdot c = -bc $$

1. Last: Multiply \( -b \) and \( -d \) (remember that multiplying two negative numbers results in a positive number)

$$ (-b) \cdot (-d) = bd $$

Step 3: Combine the terms

Now, we write all the resulting terms together in a single algebraic expression:

$$ ac - ad - bc + bd $$

Answer:

$$ ac - ad - bc + bd $$