Answer :
To simplify the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex], you can use the distributive property, also known as the FOIL method when working with polynomials. Let's simplify the expression step-by-step:
1. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
- 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 polynomial:
- 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 all the results:
[tex]\[
28x^3 - 21x^2 - 42x - 12x^2 + 9x + 18
\][/tex]
4. Combine like terms:
- The [tex]\(x^2\)[/tex] terms:
[tex]\[
-21x^2 - 12x^2 = -33x^2
\][/tex]
- The [tex]\(x\)[/tex] terms:
[tex]\[
-42x + 9x = -33x
\][/tex]
5. Final simplified expression:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
So, the correct simplification of the expression is [tex]\(\boxed{28x^3 - 33x^2 - 33x + 18}\)[/tex].
1. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
- 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 polynomial:
- 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 all the results:
[tex]\[
28x^3 - 21x^2 - 42x - 12x^2 + 9x + 18
\][/tex]
4. Combine like terms:
- The [tex]\(x^2\)[/tex] terms:
[tex]\[
-21x^2 - 12x^2 = -33x^2
\][/tex]
- The [tex]\(x\)[/tex] terms:
[tex]\[
-42x + 9x = -33x
\][/tex]
5. Final simplified expression:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
So, the correct simplification of the expression is [tex]\(\boxed{28x^3 - 33x^2 - 33x + 18}\)[/tex].
