(2x%2B3)-expand-and-simplify.jpeg "(x-1)(2x+3) Expand And Simplify")
Expanding and Simplifying the Expression (x-1)(2x+3)
In this article, we will explore how to expand and simplify the algebraic expression (x-1)(2x+3). Expansion and simplification are crucial steps in algebraic manipulations, and mastering these skills will help you tackle more complex expressions with ease.
Expanding the Expression
To expand the expression (x-1)(2x+3), we need to follow the order of operations (PEMDAS) and multiply each term in the first parentheses by each term in the second parentheses.
(x-1)(2x+3) = x(2x+3) - 1(2x+3)
Now, let's multiply each term:
x(2x+3) = 2x² + 3x -1(2x+3) = -2x - 3
So, the expanded expression is:
2x² + 3x - 2x - 3
Simplifying the Expression
Now that we have expanded the expression, our next step is to simplify it. Simplification involves combining like terms and eliminating any duplicates.
In our expanded expression, we can see that there are two terms containing x: 3x and -2x. We can combine these terms by adding their coefficients:
3x - 2x = x
So, the simplified expression becomes:
2x² + x - 3
Final Result
The final simplified expression is:
2x² + x - 3
In conclusion, expanding and simplifying the expression (x-1)(2x+3) involves multiplying each term in the first parentheses by each term in the second parentheses and then combining like terms to eliminate duplicates. The final simplified expression is 2x² + x - 3.
