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Answer :
To simplify the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex], we will use the distributive property, also known as the FOIL method for multiplying two polynomials. Here's how you can simplify it step-by-step:
1. Distribute [tex]\(7x\)[/tex] across all terms inside the second parentheses:
[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 all terms inside the second parentheses:
[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:
Start with the highest degree terms and combine like terms:
- Cubic term: [tex]\(28x^3\)[/tex]
- Quadratic terms: [tex]\(-21x^2 - 12x^2 = -33x^2\)[/tex]
- Linear terms: [tex]\(-42x + 9x = -33x\)[/tex]
- Constant term: [tex]\(18\)[/tex]
4. Write the simplified expression:
Therefore, the simplified form of the expression is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
So, the correct simplification of the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct choice is: [tex]\(28x^3 - 33x^2 - 33x + 18\)[/tex].
1. Distribute [tex]\(7x\)[/tex] across all terms inside the second parentheses:
[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 all terms inside the second parentheses:
[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:
Start with the highest degree terms and combine like terms:
- Cubic term: [tex]\(28x^3\)[/tex]
- Quadratic terms: [tex]\(-21x^2 - 12x^2 = -33x^2\)[/tex]
- Linear terms: [tex]\(-42x + 9x = -33x\)[/tex]
- Constant term: [tex]\(18\)[/tex]
4. Write the simplified expression:
Therefore, the simplified form of the expression is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
So, the correct simplification of the expression [tex]\((7x - 3)(4x^2 - 3x - 6)\)[/tex] is:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Thus, the correct choice is: [tex]\(28x^3 - 33x^2 - 33x + 18\)[/tex].
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