Answer :
Sure! Let's simplify the expression [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex] step-by-step:
1. Distribute [tex]\((4x - 3)\)[/tex] across each term in [tex]\((3x^2 - 4x - 3)\)[/tex]. This means we'll multiply [tex]\(4x\)[/tex] by each term in the second polynomial, and then do the same with [tex]\(-3\)[/tex].
2. Multiply [tex]\(4x\)[/tex] by each of the terms in [tex]\((3x^2 - 4x - 3)\)[/tex]:
[tex]\[
4x \cdot 3x^2 = 12x^3
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2
\][/tex]
[tex]\[
4x \cdot (-3) = -12x
\][/tex]
3. Multiply [tex]\(-3\)[/tex] by each of the terms in [tex]\((3x^2 - 4x - 3)\)[/tex]:
[tex]\[
-3 \cdot 3x^2 = -9x^2
\][/tex]
[tex]\[
-3 \cdot (-4x) = 12x
\][/tex]
[tex]\[
-3 \cdot (-3) = 9
\][/tex]
4. Combine all these terms together:
[tex]\[
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9
\][/tex]
5. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex]
6. Write the final simplified expression:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
Therefore, the correct simplification of [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex] is [tex]\(\boxed{12x^3 - 25x^2 + 9}\)[/tex].
1. Distribute [tex]\((4x - 3)\)[/tex] across each term in [tex]\((3x^2 - 4x - 3)\)[/tex]. This means we'll multiply [tex]\(4x\)[/tex] by each term in the second polynomial, and then do the same with [tex]\(-3\)[/tex].
2. Multiply [tex]\(4x\)[/tex] by each of the terms in [tex]\((3x^2 - 4x - 3)\)[/tex]:
[tex]\[
4x \cdot 3x^2 = 12x^3
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2
\][/tex]
[tex]\[
4x \cdot (-3) = -12x
\][/tex]
3. Multiply [tex]\(-3\)[/tex] by each of the terms in [tex]\((3x^2 - 4x - 3)\)[/tex]:
[tex]\[
-3 \cdot 3x^2 = -9x^2
\][/tex]
[tex]\[
-3 \cdot (-4x) = 12x
\][/tex]
[tex]\[
-3 \cdot (-3) = 9
\][/tex]
4. Combine all these terms together:
[tex]\[
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9
\][/tex]
5. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex]
6. Write the final simplified expression:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
Therefore, the correct simplification of [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex] is [tex]\(\boxed{12x^3 - 25x^2 + 9}\)[/tex].
