What is factor a^7-128 ?

The solution to factor a^7-128 is (a-2)(a^6+2a^5+4a^4+8a^3+16a^2+32a+64)

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factor a^7-128

factor

a^{7} - 128

(a - 2) (a^{6} + 2 a^{5} + 4 a^{4} + 8 a^{3} + 16 a^{2} + 32 a + 64)

Solution steps

a^{7} - 128

Rewrite

128

2^{7}

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

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

Simplify

(a - 2) (a^{6} + 2 a^{5} + 2^{2} a^{4} + 2^{3} a^{3} + 2^{4} a^{2} + 2^{5} a + 2^{6}) : (a - 2) (a^{6} + 2 a^{5} + 4 a^{4} + 8 a^{3} + 16 a^{2} + 32 a + 64)

= (a - 2) (a^{6} + 2 a^{5} + 4 a^{4} + 8 a^{3} + 16 a^{2} + 32 a + 64)

(3 n - 4)^{2}

(- 2 q)^{2}

32 a^{2} + 50 q^{2}

ln (0.92)

What is factor a^7-128 ?
The solution to factor a^7-128 is (a-2)(a^6+2a^5+4a^4+8a^3+16a^2+32a+64)