What is factor a^7-2187 ?

The solution to factor a^7-2187 is (a-3)(a^6+3a^5+9a^4+27a^3+81a^2+243a+729)

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factor a^7-2187

factor

a^{7} - 2187

(a - 3) (a^{6} + 3 a^{5} + 9 a^{4} + 27 a^{3} + 81 a^{2} + 243 a + 729)

Solution steps

a^{7} - 2187

Rewrite

2187

3^{7}

= a^{7} - 3^{7}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

a^{7} - 3^{7} = (a - 3) (a^{6} + 3 a^{5} + 3^{2} a^{4} + 3^{3} a^{3} + 3^{4} a^{2} + 3^{5} a + 3^{6})

= (a - 3) (a^{6} + 3 a^{5} + 3^{2} a^{4} + 3^{3} a^{3} + 3^{4} a^{2} + 3^{5} a + 3^{6})

Simplify

(a - 3) (a^{6} + 3 a^{5} + 3^{2} a^{4} + 3^{3} a^{3} + 3^{4} a^{2} + 3^{5} a + 3^{6}) : (a - 3) (a^{6} + 3 a^{5} + 9 a^{4} + 27 a^{3} + 81 a^{2} + 243 a + 729)

= (a - 3) (a^{6} + 3 a^{5} + 9 a^{4} + 27 a^{3} + 81 a^{2} + 243 a + 729)

- \frac{15}{2}

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

1 - c^{3}

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

What is factor a^7-2187 ?
The solution to factor a^7-2187 is (a-3)(a^6+3a^5+9a^4+27a^3+81a^2+243a+729)