Binomial expansion of (x+2)^4

1 answer:

N76 [4]3 years ago

4 0

The two terms are x and 2, thus, x+2 is a binomial. We have to multiply the binomial by itself four times since it is raised to 4th power.

Let us multiply x+2 by itself using Polynomial Multiplication:

(x+2)(x+2) = x^2 + 4x + 4

Taking the result, let us multiply it again by a+b:

(x^2 + 4x + 4)(x+2) = x^3 + 6x^2 + 12x + 8

And again:

(x^3 + 6x^2 + 12x + 8)(x+2) = x^4 + 8x^3 + 24x^2 + 32x +16

The binomial expansion of (x+2)^4 is x^4 + 8x^3 + 24x^2 + 32x +16

You might be interested in

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)

creativ13 [48]

Answer:

(sin^2 w + 1) / cos w.

Step-by-step explanation:

Note: sec w = 1 / cos w and csc w = 1/ sin w.

So we have:

(sec w(1 + csc^2 w)) / (csc^2 w)

= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)

= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w

= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)

= sin^2 w / cos w + 1 / cos w

= (sin^2 w + 1) / cos w.

4 0

2 years ago

NEED ASAP NEED TO RURN IN FAST!!! WILL MARK *BRAINLIEST*

Travka [436]

Answer:

Step-by-step explanation:

We know that:

-measuring a cone
-diameter: 18 units
-height: 8 units

We need to know how to find the volume of this cone. To do this, we need the equation to find the volume of a cone:
$V= \pi r^2\frac{h}{3}$ where r=radius and h=height

Upon assessing this equation we also now know that we are missing a radius.

For a circle, the radius is the distance from the midpoint, center, to the border of the circle. The diameter is the distance from the border of one circle to another, passing through the midpoint. Knowing this, we can conclude that the diameter is two times the radius.

Using this information we can figure out the radius for this cone: 9 units.

Now that we have the radius, we can plug in the rest of the numbers with the correct placements.

$V= \pi 9^2\frac{8}{3}$ square the 9 by calculating 9 times 9.