(2x%2B3).jpeg "(2x+10)(2x+3)")
Expanding the Expression (2x + 10)(2x + 3)
This expression represents the product of two binomials, (2x + 10) and (2x + 3). To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
Outer: Multiply the outer terms of each binomial: (2x) * (3) = 6x
Inner: Multiply the inner terms of each binomial: (10) * (2x) = 20x
Last: Multiply the last terms of each binomial: (10) * (3) = 30
Now we have: 4x² + 6x + 20x + 30
Finally, combine the like terms: 4x² + 26x + 30
Therefore, the expanded form of (2x + 10)(2x + 3) is 4x² + 26x + 30.
Understanding the Process
The FOIL method is a simple way to remember how to multiply binomials. It ensures that we multiply each term in the first binomial by each term in the second binomial.
This expansion is useful for various applications, including:
- Solving equations: We can set this expression equal to zero and solve for the value of 'x' to find the roots of the equation.
- Graphing functions: By expanding the expression, we can analyze the behavior of the corresponding quadratic function, including its vertex, intercepts, and concavity.
- Area calculations: This expression can represent the area of a rectangle with dimensions (2x + 10) and (2x + 3).
Remember, understanding how to expand expressions is a fundamental skill in algebra and has wide applications in various mathematical contexts.