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}), n i s o dd

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)

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

(\frac{2 a ^{3}}{b ^{4}})^{3}

z^{2} - z + 1 - i

(3 - 6) y (- 24)

\frac{( x ^{2} - 2 x - 15 )}{( x + 3 )}

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)