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

The solution to factor (t-3)^{7/2}-(t-3)^{3/2} is (t-2)(sqrt(t-3)+1)(sqrt(t-3)-1)(t-3)^{3/2}

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factor (t-3)^{7/2}-(t-3)^{3/2}

factor

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

(t - 2) (t - 3 + 1) (t - 3 - 1) (t - 3)^{\frac{3}{2}}

Solution steps

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

Rewrite

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

(t - 3)^{7}

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

Rewrite

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

(t - 3)^{3}

= (t - 3)^{7} - (t - 3)^{3}

Factor out common term

(t - 3)^{3} : (t - 3)^{3} ((t - 3)^{4} - 1)

= (t - 3)^{3} ((t - 3)^{4} - 1)

Factor

(t - 3)^{4} - 1 : ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1)

= (t - 3)^{3} ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1)

Simplify

(t - 3)^{3} ((t - 3)^{2} + 1) (t - 3 + 1) (t - 3 - 1) : (t - 3)^{3} (t - 2) (t - 3 + 1) (t - 3 - 1)

= (t - 3)^{3} (t - 2) (t - 3 + 1) (t - 3 - 1)

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

= (t - 2) (t - 3 + 1) (t - 3 - 1) (t - 3)^{\frac{3}{2}}

(p + 1)^{2} = 11 (p + 1) - 30

2^{n} + 2^{n}

4 (3 x - 5) - 4 (5 x - 2) + 3 = x + 36

- 1 - j > 1

x^{2} + 3 x + 8 = - 3 x + 3

What is factor (t-3)^{7/2}-(t-3)^{3/2} ?
The solution to factor (t-3)^{7/2}-(t-3)^{3/2} is (t-2)(sqrt(t-3)+1)(sqrt(t-3)-1)(t-3)^{3/2}