(x%2B6).jpeg "(2x+1)(x+6)")
Expanding the Expression (2x+1)(x+6)
This article will focus on expanding the algebraic expression (2x+1)(x+6). This expression represents the product of two binomials, and we will explore different methods to simplify it into a polynomial form.
Using the FOIL Method
The FOIL method is a common technique used to multiply binomials. FOIL stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
(2x+1)(x+6)
- First: (2x)(x) = 2x²
- Outer: (2x)(6) = 12x
- Inner: (1)(x) = x
- Last: (1)(6) = 6
Now we combine these terms: 2x² + 12x + x + 6
Finally, we simplify by combining like terms: 2x² + 13x + 6
Using the Distributive Property
Another method to expand the expression is to use the distributive property. This involves distributing each term of one binomial to the other binomial.
(2x+1)(x+6)
- Distribute 2x: 2x(x+6) = 2x² + 12x
- Distribute 1: 1(x+6) = x + 6
Combining the results from both distributions, we get: 2x² + 12x + x + 6
Again, we simplify by combining like terms: 2x² + 13x + 6
Conclusion
Both the FOIL method and the distributive property lead us to the same simplified expression: 2x² + 13x + 6. This polynomial represents the expanded form of the original expression (2x+1)(x+6).