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Answer :
To multiply the polynomials
[tex]\[
(8x + 9)(3x^2 + x - 1),
\][/tex]
we follow these steps:
1. Multiply every term in the first polynomial by every term in the second polynomial.
2. First, multiply [tex]\(8x\)[/tex] by each term in [tex]\(3x^2 + x - 1\)[/tex]:
[tex]\[
\begin{aligned}
8x \cdot 3x^2 &= 24x^3, \\
8x \cdot x &= 8x^2, \\
8x \cdot (-1) &= -8x.
\end{aligned}
\][/tex]
3. Next, multiply [tex]\(9\)[/tex] by each term in [tex]\(3x^2 + x - 1\)[/tex]:
[tex]\[
\begin{aligned}
9 \cdot 3x^2 &= 27x^2, \\
9 \cdot x &= 9x, \\
9 \cdot (-1) &= -9.
\end{aligned}
\][/tex]
4. Now, write down all the products:
[tex]\[
24x^3,\quad 8x^2,\quad -8x,\quad 27x^2,\quad 9x,\quad -9.
\][/tex]
5. Combine like terms:
- For [tex]\(x^3\)[/tex]: There is only one term, [tex]\(24x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(8x^2 + 27x^2 = 35x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-8x + 9x = x\)[/tex].
- For the constant term: [tex]\(-9\)[/tex].
6. The final expression is:
[tex]\[
24x^3 + 35x^2 + x - 9.
\][/tex]
Thus, the product of the two polynomials is
[tex]\[
\boxed{24x^3 + 35x^2 + x - 9}.
\][/tex]
[tex]\[
(8x + 9)(3x^2 + x - 1),
\][/tex]
we follow these steps:
1. Multiply every term in the first polynomial by every term in the second polynomial.
2. First, multiply [tex]\(8x\)[/tex] by each term in [tex]\(3x^2 + x - 1\)[/tex]:
[tex]\[
\begin{aligned}
8x \cdot 3x^2 &= 24x^3, \\
8x \cdot x &= 8x^2, \\
8x \cdot (-1) &= -8x.
\end{aligned}
\][/tex]
3. Next, multiply [tex]\(9\)[/tex] by each term in [tex]\(3x^2 + x - 1\)[/tex]:
[tex]\[
\begin{aligned}
9 \cdot 3x^2 &= 27x^2, \\
9 \cdot x &= 9x, \\
9 \cdot (-1) &= -9.
\end{aligned}
\][/tex]
4. Now, write down all the products:
[tex]\[
24x^3,\quad 8x^2,\quad -8x,\quad 27x^2,\quad 9x,\quad -9.
\][/tex]
5. Combine like terms:
- For [tex]\(x^3\)[/tex]: There is only one term, [tex]\(24x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(8x^2 + 27x^2 = 35x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-8x + 9x = x\)[/tex].
- For the constant term: [tex]\(-9\)[/tex].
6. The final expression is:
[tex]\[
24x^3 + 35x^2 + x - 9.
\][/tex]
Thus, the product of the two polynomials is
[tex]\[
\boxed{24x^3 + 35x^2 + x - 9}.
\][/tex]
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