What is the completely factored form of d^4 - 81

Step-by-step explanation:

d^4-81

(d^2)^2-(9)^2

Using formula

(d^2+9)(d^2-9)

(d - 3)(d + 3)(d² + 9)

Step-by-step explanation:

- 81 ← can be factored as a difference of squares

a² - b² = (a - b)(a + b), thus

- 81

= (d²)² - 9²

= (d² - 9)(d² + 9)

Note that d² - 9 is also a difference of square, so

= (d - 3)(d + 3)(d² + 9) ← in factored form

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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step-by-step explanation: