(2x+5)(x+1)

Jasonbradley

2 min read

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Jun 16, 2024

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Expanding and Simplifying (2x + 5)(x + 1)

This expression represents the product of two binomials: (2x + 5) and (x + 1). To simplify it, we can use the FOIL method, which stands for First, Outer, Inner, Last.

Here's how it works:

1. First: Multiply the first terms of each binomial: 2x * x = 2x²
2. Outer: Multiply the outer terms of the binomials: 2x * 1 = 2x
3. Inner: Multiply the inner terms of the binomials: 5 * x = 5x
4. Last: Multiply the last terms of each binomial: 5 * 1 = 5

Now, we combine the resulting terms:

2x² + 2x + 5x + 5

Finally, we simplify by combining the like terms (the terms with the same variable and exponent):

2x² + 7x + 5

Therefore, the simplified form of (2x + 5)(x + 1) is 2x² + 7x + 5.

Key takeaways:

• The FOIL method is a useful tool for expanding the product of two binomials.
• Remember to combine like terms after applying the FOIL method to simplify the expression.

Further exploration:

You can use this simplified expression for various purposes, such as:

• Finding the roots of a quadratic equation: Set the expression equal to zero and solve for x.
• Graphing the function: The expression represents a quadratic function, which can be graphed on a coordinate plane.
• Solving real-world problems: Quadratic expressions can be used to model various real-life situations, such as projectile motion or optimization problems.