How do you factor this completly

7x*(4x-5)^3+(4x-5)^4

I am confused by the different power of exponets and the 7x in front Can you please help me?

7x*(4x-5)^3+(4x-5)^4 factor out the common term:
(4x-5)^3 * (7x+4x-5) Then simplify the second term.

what general equation will model this problem, with a focus of 1.8, points at (1.8,5) and (1.8,-5).with the center in the orgin.

To generate an equation that satisfies the given conditions, you need to use the general equation of a conic section, specifically for a parabola. A parabola with its focus at (h, k) and a directrix given by the equation ax + by + c = 0 can be represented by the equation:

((x - h)^2 + (y - k)^2) / (4p) = (y - k)

where the value of p represents the distance between the vertex and the focus.

In this case, the focus is given as (1.8, 5) and (-1.8, -5). Since the focus is on the y-axis, the directrix will be a horizontal line passing through the point (0, -p). The value of p can be determined by finding the distance between the focus and the directrix, which is 5 units.

Now, let's plug in the given values into the equation:

((x - 0)^2 + (y - (-p))^2) / (4p) = (y - (-p))

Simplify the equation by multiplying both sides by 4p:

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

Since the center is at the origin (0, 0), h and k are both zero. Also, p is equal to 5. Therefore, the equation becomes:

x^2 + (y + 5)^2 = 20(y + 5)