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Answer :
To find the product of [tex]\((x^2 + 3x + 9)\)[/tex] and [tex]\((x - 3)\)[/tex], follow these steps:
1. Write down the expression to be multiplied:
[tex]\[
(x^2 + 3x + 9)(x - 3)
\][/tex]
2. Use the distributive property (also known as the FOIL method in this case) to expand the expression:
Each term in the first polynomial will multiply each term in the second polynomial.
3. Multiply each term in [tex]\(x^2 + 3x + 9\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
3x \cdot x = 3x^2
\][/tex]
[tex]\[
9 \cdot x = 9x
\][/tex]
4. Multiply each term in [tex]\(x^2 + 3x + 9\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
[tex]\[
3x \cdot (-3) = -9x
\][/tex]
[tex]\[
9 \cdot (-3) = -27
\][/tex]
5. Now, combine all the products:
[tex]\[
x^3 + 3x^2 + 9x - 3x^2 - 9x - 27
\][/tex]
6. Combine like terms (terms with the same power of [tex]\(x\)[/tex]):
[tex]\[
x^3 + (3x^2 - 3x^2) + (9x - 9x) - 27
\][/tex]
[tex]\[
x^3 - 27
\][/tex]
So, the product of [tex]\((x^2 + 3x + 9)\)[/tex] and [tex]\((x - 3)\)[/tex] is:
[tex]\[
x^3 - 27
\][/tex]
The correct option is:
(1) [tex]\(x^3 - 27\)[/tex]
1. Write down the expression to be multiplied:
[tex]\[
(x^2 + 3x + 9)(x - 3)
\][/tex]
2. Use the distributive property (also known as the FOIL method in this case) to expand the expression:
Each term in the first polynomial will multiply each term in the second polynomial.
3. Multiply each term in [tex]\(x^2 + 3x + 9\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
3x \cdot x = 3x^2
\][/tex]
[tex]\[
9 \cdot x = 9x
\][/tex]
4. Multiply each term in [tex]\(x^2 + 3x + 9\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
[tex]\[
3x \cdot (-3) = -9x
\][/tex]
[tex]\[
9 \cdot (-3) = -27
\][/tex]
5. Now, combine all the products:
[tex]\[
x^3 + 3x^2 + 9x - 3x^2 - 9x - 27
\][/tex]
6. Combine like terms (terms with the same power of [tex]\(x\)[/tex]):
[tex]\[
x^3 + (3x^2 - 3x^2) + (9x - 9x) - 27
\][/tex]
[tex]\[
x^3 - 27
\][/tex]
So, the product of [tex]\((x^2 + 3x + 9)\)[/tex] and [tex]\((x - 3)\)[/tex] is:
[tex]\[
x^3 - 27
\][/tex]
The correct option is:
(1) [tex]\(x^3 - 27\)[/tex]
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