What is factor (x-7)^{7/2}-49(x-7)^{3/2} ?

The solution to factor (x-7)^{7/2}-49(x-7)^{3/2} is x(x-14)(x-7)^{3/2}

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factor (x-7)^{7/2}-49(x-7)^{3/2}

factor

(x - 7)^{\frac{7}{2}} - 49 (x - 7)^{\frac{3}{2}}

x (x - 14) (x - 7)^{\frac{3}{2}}

Solution steps

(x - 7)^{\frac{7}{2}} - 49 (x - 7)^{\frac{3}{2}}

Rewrite

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

(x - 7)^{7}

= (x - 7)^{7} - 49 (x - 7)^{\frac{3}{2}}

Rewrite

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

(x - 7)^{3}

= (x - 7)^{7} - 49 (x - 7)^{3}

Factor out common term

(x - 7)^{3} : (x - 7)^{3} ((x - 7)^{4} - 49)

= (x - 7)^{3} ((x - 7)^{4} - 49)

Factor

(x - 7)^{4} - 49 : ((x - 7)^{2} + 7) ((x - 7)^{2} - 7)

= (x - 7)^{3} ((x - 7)^{2} + 7) ((x - 7)^{2} - 7)

Simplify

(x - 7)^{3} ((x - 7)^{2} + 7) ((x - 7)^{2} - 7) : x (x - 7)^{3} (x - 14)

= x (x - 7)^{3} (x - 14)

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

= x (x - 14) (x - 7)^{\frac{3}{2}}

12 x^{3} + 48 x^{2} + 48 x

\frac{a}{- 8} + 15 > 23

232

25 + 5

What is factor (x-7)^{7/2}-49(x-7)^{3/2} ?
The solution to factor (x-7)^{7/2}-49(x-7)^{3/2} is x(x-14)(x-7)^{3/2}