(2x-7).jpeg "(2x+3)(2x-7)")
Expanding the Expression: (2x + 3)(2x - 7)
This article will explore the process of expanding the algebraic expression (2x + 3)(2x - 7).
Understanding the Expression
The expression (2x + 3)(2x - 7) represents the product of two binomials. Binomials are algebraic expressions with two terms.
Expanding Using the FOIL Method
The FOIL method is a popular technique for expanding the product of two binomials. FOIL stands for First, Outer, Inner, Last. Here's how it works:
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of the binomials: (2x) * (-7) = -14x
- Inner: Multiply the inner terms of the binomials: (3) * (2x) = 6x
- Last: Multiply the last terms of each binomial: (3) * (-7) = -21
Now, combine the results: 4x² - 14x + 6x - 21
Simplifying the Expression
The final step is to simplify the expression by combining like terms:
4x² - 8x - 21
Conclusion
By using the FOIL method, we have expanded the expression (2x + 3)(2x - 7) to obtain the simplified form: 4x² - 8x - 21. This process is essential for understanding and manipulating algebraic expressions.