How do you multiply #(v ^ { 2} - 7v - 4) ( 6v ^ { 2} - 3v - 7)#?

Question

Avery Alexander · Accepted Answer

#6v^4-45v^3-10v^2+61v+28#

Let's get more:

#6v^4color(red)(-3v^3)color(green)(-7v^2)color(red)(-42v^3)color(green)(+21v^2)color(blue)(+49v)color(green)(-24v^2)color(blue)(+12v)+28#

Let's add up the similar terms:

#6v^4-45v^3-10v^2+61v+28#

Genesis Allen · Answer

undefined To multiply the given expressions, you can use the distributive property and combine like terms. Here are the steps:

1. Multiply the first terms of each binomial: (v^2)(6v^2) = 6v^4.
2. Multiply the first terms of each binomial: (v^2)(-3v) = -3v^3.
3. Multiply the first terms of each binomial: (v^2)(-7) = -7v^2.
4. Multiply the second terms of each binomial: (-7v)(6v^2) = -42v^3.
5. Multiply the second terms of each binomial: (-7v)(-3v) = 21v^2.
6. Multiply the second terms of each binomial: (-7v)(-7) = 49v.
7. Multiply the third terms of each binomial: (-4)(6v^2) = -24v^2.
8. Multiply the third terms of each binomial: (-4)(-3v) = 12v.
9. Multiply the third terms of each binomial: (-4)(-7) = 28.

10. Combine all the like terms obtained in the previous steps:
6v^4 - 3v^3 - 7v^2 - 42v^3 + 21v^2 + 49v - 24v^2 + 12v + 28.

11. Simplify the expression by combining like terms:
6v^4 - 45v^3 + 10v^2 + 61v + 28.

Therefore, the product of (v^2 - 7v - 4) and (6v^2 - 3v - 7) is 6v^4 - 45v^3 + 10v^2 + 61v + 28.