To simplify the expression [tex]\( 3x^2 - 2x(3x - 4) \)[/tex], we need to follow a series of steps involving basic algebraic operations. Let's break down the steps and compute the simplified expression:
1. Distribute the multiplication inside the second term:
[tex]\[
-2x(3x - 4)
\][/tex]
Distributing [tex]\(-2x\)[/tex] inside the parenthesis:
[tex]\[
-2x \cdot 3x + (-2x) \cdot (-4)
\][/tex]
[tex]\[
-6x^2 + 8x
\][/tex]
2. Simplify the original expression by combining like terms:
The original expression is:
[tex]\[
3x^2 - 2x(3x - 4)
\][/tex]
Substituting the distributed result:
[tex]\[
3x^2 - (6x^2 - 8x)
\][/tex]
3. Distribute the negative sign:
[tex]\[
3x^2 - 6x^2 + 8x
\][/tex]
4. Combine like terms:
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
(3x^2 - 6x^2) + 8x
\][/tex]
[tex]\[
-3x^2 + 8x
\][/tex]
After simplifying, we see the simplified expression is [tex]\(-3x^2 + 8x\)[/tex].
Given the choices:
- A: [tex]\( 3x^2 - 8 \)[/tex]
- B: [tex]\( -3x^2 + 8x \)[/tex]
- C: [tex]\( -3x^2 - 8x \)[/tex]
- D: [tex]\( 3x^2 - 6x + 8 \)[/tex]
The correct answer is:
B) [tex]\(-3x^2 + 8x\)[/tex].
