Answer :
To simplify the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex], we'll use the distributive property, which involves multiplying each term in the first expression by each term in the second expression, and then combining like terms. Let's go through the steps:
1. Distribute [tex]\(7x\)[/tex] to each term in the second expression:
- Multiply [tex]\(7x\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
7x \cdot 4x^2 = 28x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7x \cdot (-6) = -42x
\][/tex]
2. Distribute [tex]\(-3\)[/tex] to each term in the second expression:
- Multiply [tex]\(-3\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
-3 \cdot 4x^2 = -12x^2
\][/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
-3 \cdot (-3x) = 9x
\][/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
-3 \cdot (-6) = 18
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] term:
[tex]\[
28x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-21x^2 - 12x^2 = -33x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-42x + 9x = -33x
\][/tex]
- The constant term is:
[tex]\[
18
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct simplification of the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
1. Distribute [tex]\(7x\)[/tex] to each term in the second expression:
- Multiply [tex]\(7x\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
7x \cdot 4x^2 = 28x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7x \cdot (-6) = -42x
\][/tex]
2. Distribute [tex]\(-3\)[/tex] to each term in the second expression:
- Multiply [tex]\(-3\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
-3 \cdot 4x^2 = -12x^2
\][/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
-3 \cdot (-3x) = 9x
\][/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
-3 \cdot (-6) = 18
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] term:
[tex]\[
28x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-21x^2 - 12x^2 = -33x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-42x + 9x = -33x
\][/tex]
- The constant term is:
[tex]\[
18
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct simplification of the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
