Quick Math Expansion
Enter expression in this form
Example: (2x + 3)(x - 4).
Expansion of Algebraic Expressions
Expanding algebraic expressions involves multiplying out the terms within parentheses or simplifying expressions into a series of simpler terms. This process is essential for solving equations, factoring, and understanding relationships between variables.
Steps for Expansion
1. Apply Distributive Property: Distribute terms across parentheses or brackets.
2. Multiply Binomials: Multiply two binomials using the FOIL method (First, Outer, Inner, Last).
3. Expand Powers: Expand expressions involving powers or exponents.
4. Combine Like Terms: Simplify the expanded expression by combining like terms.
Detailed Example
Let’s expand the expression \((2x + 3)(x – 4)\).
Steps:
1. Apply Distributive Property (FOIL Method):
– Multiply the terms in each pair:
\[(2x + 3)(x – 4) = 2x \cdot x + 2x \cdot (-4) + 3 \cdot x + 3 \cdot (-4)\]
2. Simplify Each Term:
– Calculate each multiplication:
\[= 2x^2 – 8x + 3x – 12\]
3. Combine Like Terms:
– Combine the middle terms:
\[= 2x^2 – 5x – 12\]
Verification
To verify, expand the expression and check if it matches the calculated form:
Original: \((2x + 3)(x – 4)\).
Expanded: \(2x^2 – 5x – 12\).
The expanded and calculated forms match, confirming that the expansion was performed correctly.
Expanding algebraic expressions is a fundamental skill that helps in manipulating equations, factoring polynomials, and solving problems in algebra. Mastering expansion techniques enhances understanding of algebraic relationships and prepares for more advanced mathematical concepts. Practice expanding various expressions to improve problem-solving abilities and algebraic proficiency.
