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Expanding the Expression (x+4)(x+6)
This article explores the expansion of the expression (x+4)(x+6), a common algebraic operation that demonstrates the distributive property and leads to a quadratic expression.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In our case, we need to distribute each term in the first set of parentheses to both terms in the second set:
Step 1: Multiply the first term of the first set of parentheses (x) with both terms in the second set:
- x * x = x²
- x * 6 = 6x
Step 2: Multiply the second term of the first set of parentheses (4) with both terms in the second set:
- 4 * x = 4x
- 4 * 6 = 24
Combining the Terms
Now, we have four terms: x², 6x, 4x, and 24. We can combine the like terms (6x and 4x) to simplify the expression:
Step 3: x² + 6x + 4x + 24
Step 4: x² + 10x + 24
Conclusion
Therefore, the expanded form of (x+4)(x+6) is x² + 10x + 24. This process demonstrates the fundamental principle of the distributive property and showcases the steps involved in expanding binomials.