Answer :
We want to multiply the two polynomials:
[tex]$$
(8x + 9)(3x^2 + x - 1)
$$[/tex]
Step 1: Distribute each term of the first polynomial across the second polynomial.
1. Multiply the first term [tex]$8x$[/tex] by each term in the second polynomial:
- [tex]$8x \times 3x^2 = 24x^3$[/tex]
- [tex]$8x \times x = 8x^2$[/tex]
- [tex]$8x \times (-1) = -8x$[/tex]
Step 2: Now, multiply the second term [tex]$9$[/tex] by each term in the second polynomial:
- [tex]$9 \times 3x^2 = 27x^2$[/tex]
- [tex]$9 \times x = 9x$[/tex]
- [tex]$9 \times (-1) = -9$[/tex]
Step 3: Write down all the results:
[tex]$$
24x^3,\quad 8x^2,\quad -8x,\quad 27x^2,\quad 9x,\quad -9
$$[/tex]
Step 4: Combine like terms. Group the terms by the power of [tex]$x$[/tex]:
- For [tex]$x^3$[/tex]: There is only [tex]$24x^3$[/tex].
- For [tex]$x^2$[/tex]: Combine [tex]$8x^2$[/tex] and [tex]$27x^2$[/tex], which gives
[tex]$$
8x^2 + 27x^2 = 35x^2.
$$[/tex]
- For [tex]$x$[/tex]: Combine [tex]$-8x$[/tex] and [tex]$9x$[/tex], which gives
[tex]$$
-8x + 9x = x.
$$[/tex]
- The constant term is [tex]$-9$[/tex].
Step 5: Write the final result:
[tex]$$
24x^3 + 35x^2 + x - 9.
$$[/tex]
Thus, the product of the polynomials is
[tex]$$
(8x+9)(3x^2+x-1) = 24x^3+35x^2+x-9.
$$[/tex]
[tex]$$
(8x + 9)(3x^2 + x - 1)
$$[/tex]
Step 1: Distribute each term of the first polynomial across the second polynomial.
1. Multiply the first term [tex]$8x$[/tex] by each term in the second polynomial:
- [tex]$8x \times 3x^2 = 24x^3$[/tex]
- [tex]$8x \times x = 8x^2$[/tex]
- [tex]$8x \times (-1) = -8x$[/tex]
Step 2: Now, multiply the second term [tex]$9$[/tex] by each term in the second polynomial:
- [tex]$9 \times 3x^2 = 27x^2$[/tex]
- [tex]$9 \times x = 9x$[/tex]
- [tex]$9 \times (-1) = -9$[/tex]
Step 3: Write down all the results:
[tex]$$
24x^3,\quad 8x^2,\quad -8x,\quad 27x^2,\quad 9x,\quad -9
$$[/tex]
Step 4: Combine like terms. Group the terms by the power of [tex]$x$[/tex]:
- For [tex]$x^3$[/tex]: There is only [tex]$24x^3$[/tex].
- For [tex]$x^2$[/tex]: Combine [tex]$8x^2$[/tex] and [tex]$27x^2$[/tex], which gives
[tex]$$
8x^2 + 27x^2 = 35x^2.
$$[/tex]
- For [tex]$x$[/tex]: Combine [tex]$-8x$[/tex] and [tex]$9x$[/tex], which gives
[tex]$$
-8x + 9x = x.
$$[/tex]
- The constant term is [tex]$-9$[/tex].
Step 5: Write the final result:
[tex]$$
24x^3 + 35x^2 + x - 9.
$$[/tex]
Thus, the product of the polynomials is
[tex]$$
(8x+9)(3x^2+x-1) = 24x^3+35x^2+x-9.
$$[/tex]
