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Answer :
To simplify the expression [tex]\((7x-3)(4x^2-3x-6)\)[/tex], let's use the distributive property to expand it step by step.
1. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
[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] to each term in the second polynomial:
[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 formed by distribution:
[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]
So the expression becomes:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Therefore, the correct simplification of the expression [tex]\((7x-3)(4x^2-3x-6)\)[/tex] is [tex]\(\boxed{28x^3 - 33x^2 - 33x + 18}\)[/tex].
1. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
[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] to each term in the second polynomial:
[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 formed by distribution:
[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]
So the expression becomes:
[tex]\[
28x^3 - 33x^2 - 33x + 18
\][/tex]
Therefore, the correct simplification of the expression [tex]\((7x-3)(4x^2-3x-6)\)[/tex] is [tex]\(\boxed{28x^3 - 33x^2 - 33x + 18}\)[/tex].
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