Answer :
To multiply the polynomials
[tex]$$
(8x^2 + 6x + 8)(6x - 5),
$$[/tex]
we use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.
1. Multiply the first term [tex]$8x^2$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
8x^2 \cdot 6x = 48x^3,\quad 8x^2 \cdot (-5) = -40x^2.
$$[/tex]
So, the combined result is
[tex]$$
48x^3 - 40x^2.
$$[/tex]
2. Multiply the second term [tex]$6x$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
6x \cdot 6x = 36x^2,\quad 6x \cdot (-5) = -30x.
$$[/tex]
So, we get
[tex]$$
36x^2 - 30x.
$$[/tex]
3. Multiply the third term [tex]$8$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
8 \cdot 6x = 48x,\quad 8 \cdot (-5) = -40.
$$[/tex]
So, we obtain
[tex]$$
48x - 40.
$$[/tex]
4. Now, combine the obtained expressions:
- The [tex]$x^3$[/tex] term is: [tex]$$48x^3.$$[/tex]
- The [tex]$x^2$[/tex] terms are: [tex]$$-40x^2 + 36x^2 = -4x^2.$$[/tex]
- The [tex]$x$[/tex] terms are: [tex]$$-30x + 48x = 18x.$$[/tex]
- The constant term is: [tex]$$-40.$$[/tex]
Therefore, the final result of the multiplication is:
[tex]$$
48x^3 - 4x^2 + 18x - 40.
$$[/tex]
This corresponds to option A.
[tex]$$
(8x^2 + 6x + 8)(6x - 5),
$$[/tex]
we use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.
1. Multiply the first term [tex]$8x^2$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
8x^2 \cdot 6x = 48x^3,\quad 8x^2 \cdot (-5) = -40x^2.
$$[/tex]
So, the combined result is
[tex]$$
48x^3 - 40x^2.
$$[/tex]
2. Multiply the second term [tex]$6x$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
6x \cdot 6x = 36x^2,\quad 6x \cdot (-5) = -30x.
$$[/tex]
So, we get
[tex]$$
36x^2 - 30x.
$$[/tex]
3. Multiply the third term [tex]$8$[/tex] by each term in [tex]$(6x-5)$[/tex]:
[tex]$$
8 \cdot 6x = 48x,\quad 8 \cdot (-5) = -40.
$$[/tex]
So, we obtain
[tex]$$
48x - 40.
$$[/tex]
4. Now, combine the obtained expressions:
- The [tex]$x^3$[/tex] term is: [tex]$$48x^3.$$[/tex]
- The [tex]$x^2$[/tex] terms are: [tex]$$-40x^2 + 36x^2 = -4x^2.$$[/tex]
- The [tex]$x$[/tex] terms are: [tex]$$-30x + 48x = 18x.$$[/tex]
- The constant term is: [tex]$$-40.$$[/tex]
Therefore, the final result of the multiplication is:
[tex]$$
48x^3 - 4x^2 + 18x - 40.
$$[/tex]
This corresponds to option A.
