Answer :
To simplify the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex], we'll use the distributive property to expand it step-by-step.
1. Distribute [tex]\(7x\)[/tex] across the second expression:
- [tex]\(7x \cdot 4x^2 = 28x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
- [tex]\(7x \cdot (-6) = -42x\)[/tex]
2. Distribute [tex]\(-3\)[/tex] across the second expression:
- [tex]\(-3 \cdot 4x^2 = -12x^2\)[/tex]
- [tex]\(-3 \cdot (-3x) = 9x\)[/tex]
- [tex]\(-3 \cdot (-6) = 18\)[/tex]
3. Combine all the terms obtained:
[tex]\[
28x^3 - 21x^2 - 42x - 12x^2 + 9x + 18
\][/tex]
4. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-21x^2 - 12x^2 = -33x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-42x + 9x = -33x\)[/tex]
- The constant term: [tex]\(18\)[/tex]
5. Write the simplified expression:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct answer is option d: [tex]\(28x^3 - 33x^2 - 33x + 18\)[/tex].
1. Distribute [tex]\(7x\)[/tex] across the second expression:
- [tex]\(7x \cdot 4x^2 = 28x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
- [tex]\(7x \cdot (-6) = -42x\)[/tex]
2. Distribute [tex]\(-3\)[/tex] across the second expression:
- [tex]\(-3 \cdot 4x^2 = -12x^2\)[/tex]
- [tex]\(-3 \cdot (-3x) = 9x\)[/tex]
- [tex]\(-3 \cdot (-6) = 18\)[/tex]
3. Combine all the terms obtained:
[tex]\[
28x^3 - 21x^2 - 42x - 12x^2 + 9x + 18
\][/tex]
4. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-21x^2 - 12x^2 = -33x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-42x + 9x = -33x\)[/tex]
- The constant term: [tex]\(18\)[/tex]
5. Write the simplified expression:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct answer is option d: [tex]\(28x^3 - 33x^2 - 33x + 18\)[/tex].
