What is factor (x-4)^{7/2}-16(x-4)^{3/2} ?

The solution to factor (x-4)^{7/2}-16(x-4)^{3/2} is x(sqrt(x-4)+2)(sqrt(x-4)-2)(x-4)^{3/2}

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factor (x-4)^{7/2}-16(x-4)^{3/2}

factor

(x - 4)^{\frac{7}{2}} - 16 (x - 4)^{\frac{3}{2}}

x (x - 4 + 2) (x - 4 - 2) (x - 4)^{\frac{3}{2}}

Solution steps

(x - 4)^{\frac{7}{2}} - 16 (x - 4)^{\frac{3}{2}}

Rewrite

(x - 4)^{\frac{7}{2}}

(x - 4)^{7}

= (x - 4)^{7} - 16 (x - 4)^{\frac{3}{2}}

Rewrite

(x - 4)^{\frac{3}{2}}

(x - 4)^{3}

= (x - 4)^{7} - 16 (x - 4)^{3}

Factor out common term

(x - 4)^{3} : (x - 4)^{3} ((x - 4)^{4} - 16)

= (x - 4)^{3} ((x - 4)^{4} - 16)

Factor

(x - 4)^{4} - 16 : ((x - 4)^{2} + 4) (x - 4 + 2) (x - 4 - 2)

= (x - 4)^{3} ((x - 4)^{2} + 4) (x - 4 + 2) (x - 4 - 2)

Simplify

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

= x (x - 4)^{3} (x - 4 + 2) (x - 4 - 2)

(x - 4)^{3} = (x - 4)^{\frac{3}{2}}

= x (x - 4 + 2) (x - 4 - 2) (x - 4)^{\frac{3}{2}}

∣ - 3 x + 2 ∣ = x + 6

89 x^{2} + 38 x - 45 = 0

1 + 2

7 x - 7 = 2 x - 1

5 (2 + x) - x = 10 + 4 (x + 1)

What is factor (x-4)^{7/2}-16(x-4)^{3/2} ?
The solution to factor (x-4)^{7/2}-16(x-4)^{3/2} is x(sqrt(x-4)+2)(sqrt(x-4)-2)(x-4)^{3/2}