What is factor (x-5)^{7/2}-25(x-5)^{3/2} ?

The solution to factor (x-5)^{7/2}-25(x-5)^{3/2} is x(x-10)(x-5)^{3/2}

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factor (x-5)^{7/2}-25(x-5)^{3/2}

factor

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

x (x - 10) (x - 5)^{\frac{3}{2}}

Solution steps

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

Rewrite

(x - 5)^{\frac{7}{2}}

(x - 5)^{7}

= (x - 5)^{7} - 25 (x - 5)^{\frac{3}{2}}

Rewrite

(x - 5)^{\frac{3}{2}}

(x - 5)^{3}

= (x - 5)^{7} - 25 (x - 5)^{3}

Factor out common term

(x - 5)^{3} : (x - 5)^{3} ((x - 5)^{4} - 25)

= (x - 5)^{3} ((x - 5)^{4} - 25)

Factor

(x - 5)^{4} - 25 : ((x - 5)^{2} + 5) ((x - 5)^{2} - 5)

= (x - 5)^{3} ((x - 5)^{2} + 5) ((x - 5)^{2} - 5)

Simplify

(x - 5)^{3} ((x - 5)^{2} + 5) ((x - 5)^{2} - 5) : x (x - 5)^{3} (x - 10)

= x (x - 5)^{3} (x - 10)

(x - 5)^{3} = (x - 5)^{\frac{3}{2}}

= x (x - 10) (x - 5)^{\frac{3}{2}}

x^{2} + (- \frac{1}{4})^{2} = 1^{2}

5 x - (x + 1) = 5 - 2 x

\frac{3 + x}{3 - x} \geq 1

\frac{c}{c ^{2} - d ^{2}} + \frac{d}{c ^{2}}

∣ m ∣ + 2 = 11

What is factor (x-5)^{7/2}-25(x-5)^{3/2} ?
The solution to factor (x-5)^{7/2}-25(x-5)^{3/2} is x(x-10)(x-5)^{3/2}