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

The solution to factor (x-3)^{7/2}-9(x-3)^{3/2} is x(x-6)(x-3)^{3/2}

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

factor

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

x (x - 6) (x - 3)^{\frac{3}{2}}

Solution steps

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

Rewrite

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

(x - 3)^{7}

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

Rewrite

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

(x - 3)^{3}

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

Factor out common term

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

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

Factor

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

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

Simplify

(x - 3)^{3} ((x - 3)^{2} + 3) ((x - 3)^{2} - 3) : x (x - 3)^{3} (x - 6)

= x (x - 3)^{3} (x - 6)

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

= x (x - 6) (x - 3)^{\frac{3}{2}}

\frac{x + 2}{x + 3} < 0

a^{2} - b^{2} + 4 a - 4 b

r > 15 - 2 r

2 x^{2} - 17 x + 8

9 y^{2} + 5 = - 76

What is factor (x-3)^{7/2}-9(x-3)^{3/2} ?
The solution to factor (x-3)^{7/2}-9(x-3)^{3/2} is x(x-6)(x-3)^{3/2}