What is factor (x-9)^{7/2}-81(x-9)^{3/2} ?

The solution to factor (x-9)^{7/2}-81(x-9)^{3/2} is x(sqrt(x-9)+3)(sqrt(x-9)-3)(x-9)^{3/2}

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factor (x-9)^{7/2}-81(x-9)^{3/2}

factor

(x - 9)^{\frac{7}{2}} - 81 (x - 9)^{\frac{3}{2}}

x (x - 9 + 3) (x - 9 - 3) (x - 9)^{\frac{3}{2}}

Solution steps

(x - 9)^{\frac{7}{2}} - 81 (x - 9)^{\frac{3}{2}}

Rewrite

(x - 9)^{\frac{7}{2}}

(x - 9)^{7}

= (x - 9)^{7} - 81 (x - 9)^{\frac{3}{2}}

Rewrite

(x - 9)^{\frac{3}{2}}

(x - 9)^{3}

= (x - 9)^{7} - 81 (x - 9)^{3}

Factor out common term

(x - 9)^{3} : (x - 9)^{3} ((x - 9)^{4} - 81)

= (x - 9)^{3} ((x - 9)^{4} - 81)

Factor

(x - 9)^{4} - 81 : ((x - 9)^{2} + 9) (x - 9 + 3) (x - 9 - 3)

= (x - 9)^{3} ((x - 9)^{2} + 9) (x - 9 + 3) (x - 9 - 3)

Simplify

(x - 9)^{3} ((x - 9)^{2} + 9) (x - 9 + 3) (x - 9 - 3) : x (x - 9)^{3} (x - 9 + 3) (x - 9 - 3)

= x (x - 9)^{3} (x - 9 + 3) (x - 9 - 3)

(x - 9)^{3} = (x - 9)^{\frac{3}{2}}

= x (x - 9 + 3) (x - 9 - 3) (x - 9)^{\frac{3}{2}}

15 + 2 x \geq - x + 33

(- 2)^{- 3}

729 - 16 t^{2}

\frac{1}{7} - \frac{1}{9}

2 x^{3} - 5 x^{2} + 3 x - 2

What is factor (x-9)^{7/2}-81(x-9)^{3/2} ?
The solution to factor (x-9)^{7/2}-81(x-9)^{3/2} is x(sqrt(x-9)+3)(sqrt(x-9)-3)(x-9)^{3/2}