To solve the expression [tex]\(3 \cdot (2x^2 - 4x + 9)\)[/tex] step-by-step, let's distribute the factor outside the parentheses, which is [tex]\(3\)[/tex], to each term inside the parentheses: [tex]\(2x^2\)[/tex], [tex]\(-4x\)[/tex], and [tex]\(9\)[/tex].
1. First term: Multiply [tex]\(3\)[/tex] by [tex]\(2x^2\)[/tex].
[tex]\[
3 \cdot 2x^2 = 6x^2
\][/tex]
2. Second term: Multiply [tex]\(3\)[/tex] by [tex]\(-4x\)[/tex].
[tex]\[
3 \cdot (-4x) = -12x
\][/tex]
3. Third term: Multiply [tex]\(3\)[/tex] by [tex]\(9\)[/tex].
[tex]\[
3 \cdot 9 = 27
\][/tex]
Now, combine all the results from each step:
[tex]\[
6x^2 - 12x + 27
\][/tex]
So the expression [tex]\(3 \cdot (2x^2 - 4x + 9)\)[/tex] expands to:
[tex]\[
6x^2 - 12x + 27
\][/tex]
