What is factor m^7+a^7x^7 ?

The solution to factor m^7+a^7x^7 is (m+ax)(m^6-m^5ax+m^4a^2x^2-m^3a^3x^3+m^2a^4x^4-ma^5x^5+a^6x^6)

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factor m^7+a^7x^7

factor

m^{7} + a^{7} x^{7}

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

Solution steps

m^{7} + a^{7} x^{7}

Rewrite

a^{7} x^{7}

(a x)^{7}

= m^{7} + (a x)^{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 is odd

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

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

Simplify

(m + a x) (m^{6} - m^{5} a x + m^{4} (a x)^{2} - m^{3} (a x)^{3} + m^{2} (a x)^{4} - m (a x)^{5} + (a x)^{6}) : (m + a x) (m^{6} - m^{5} a x + m^{4} a^{2} x^{2} - m^{3} a^{3} x^{3} + m^{2} a^{4} x^{4} - m a^{5} x^{5} + a^{6} x^{6})

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

(x + 3)^{3} - 8

A u (N O^{3}) 3

0.064 x^{27} - 1.331 b^{15}

\frac{d}{d t} ((x) (t cos (t)))

3 a^{2} - 9 ab - 5 a c + 15 b c

What is factor m^7+a^7x^7 ?
The solution to factor m^7+a^7x^7 is (m+ax)(m^6-m^5ax+m^4a^2x^2-m^3a^3x^3+m^2a^4x^4-ma^5x^5+a^6x^6)