Absolutely, let's work on rewriting the expression [tex]\(2(x+3)(x-1)\)[/tex] in its standard form, which is [tex]\(ax^2 + bx + c\)[/tex].
1. Start by identifying the original expression:
[tex]\[
2(x+3)(x-1)
\][/tex]
2. Distribute the factors:
First, let's distribute the [tex]\(x\)[/tex] and constant terms inside the parentheses [tex]\((x+3)\)[/tex] and [tex]\((x-1)\)[/tex].
[tex]\[
(x+3)(x-1) = x(x) + x(-1) + 3(x) + 3(-1)
\][/tex]
3. Perform the multiplication:
[tex]\[
x^2 - x + 3x - 3
\][/tex]
4. Combine like terms:
[tex]\[
x^2 + 2x - 3
\][/tex]
5. Now, multiply this result by 2:
[tex]\[
2(x^2 + 2x - 3)
\][/tex]
6. Distribute the 2 across all terms inside the parentheses:
[tex]\[
2 \cdot x^2 + 2 \cdot 2x + 2 \cdot (-3)
\][/tex]
7. Simplify the multiplication:
[tex]\[
2x^2 + 4x - 6
\][/tex]
So, the standard form of [tex]\(2(x+3)(x-1)\)[/tex] is:
[tex]\[
2x^2 + 4x - 6
\][/tex]
This is the expanded form of the given expression.
