Answer :
Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex].
Here's how you can do it step by step:
1. Distribute [tex]\(-4x^2\)[/tex] to both terms in the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] with [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] with [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
(Remember: multiplying two negative numbers gives a positive result.)
2. Combine the results from the distribution:
The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
From the given options, this corresponds to option D: [tex]\(-12x^3 + 28x^2\)[/tex].
Here's how you can do it step by step:
1. Distribute [tex]\(-4x^2\)[/tex] to both terms in the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] with [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] with [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
(Remember: multiplying two negative numbers gives a positive result.)
2. Combine the results from the distribution:
The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
From the given options, this corresponds to option D: [tex]\(-12x^3 + 28x^2\)[/tex].
