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})

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})

a c + c d - ab - b d

(arctan (x))^{2}

[(3 x - y) + 2 x^{2}] [- 3 z + (3 x - y)]

6 a x - y + 2 a y - 3 x

6 a x - y + 2 a y - 3 x

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)