To simplify the expression [tex]\((x - 1)(2x + 3)\)[/tex], we will use the distributive property, which states that for any three numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], the expression [tex]\(a(b + c)\)[/tex] can be expanded to [tex]\(ab + ac\)[/tex]. This property can be applied here with [tex]\((x - 1)\)[/tex] being distributed across both terms in [tex]\((2x + 3)\)[/tex].
Here are the steps:
1. Distribute [tex]\(x\)[/tex] across the terms inside the second parenthesis:
[tex]\[
x \cdot 2x + x \cdot 3 = 2x^2 + 3x
\][/tex]
2. Distribute [tex]\(-1\)[/tex] across the terms inside the second parenthesis:
[tex]\[
-1 \cdot 2x + -1 \cdot 3 = -2x - 3
\][/tex]
3. Combine the results from both distributions:
[tex]\[
(2x^2 + 3x) + (-2x - 3)
\][/tex]
4. Combine like terms:
- Combine [tex]\(3x\)[/tex] and [tex]\(-2x\)[/tex] which results in [tex]\(x\)[/tex].
Thus, the simplified expression is:
[tex]\[
2x^2 + x - 3
\][/tex]
Therefore, [tex]\((x - 1)(2x + 3)\)[/tex] simplifies to [tex]\(2x^2 + x - 3\)[/tex].
