Sure, let's simplify the polynomial expression [tex]\(-5 x^2 (6 x - 1)\)[/tex] step-by-step using the distributive property.
1. Distribute the [tex]\(-5 x^2\)[/tex] term across the terms inside the parentheses:
This means we will multiply [tex]\(-5 x^2\)[/tex] by each term inside the parentheses separately.
2. First, multiply [tex]\(-5 x^2\)[/tex] by [tex]\(6 x\)[/tex]:
[tex]\[
-5 x^2 \cdot 6 x = -30 x^3
\][/tex]
3. Next, multiply [tex]\(-5 x^2\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
-5 x^2 \cdot (-1) = 5 x^2
\][/tex]
4. Combine the results:
So, the expression [tex]\(-5 x^2 (6 x - 1)\)[/tex] simplifies to:
[tex]\[
-30 x^3 + 5 x^2
\][/tex]
Therefore, the simplified polynomial expression is:
[tex]\[
-30 x^3 + 5 x^2
\][/tex]
