The expression x3(x−y)7−y3(x−y)7 can be rewritten as (x−y)m(x2+y2+nxy). What is the value of m ?

The value of m is 8

The expression is given as:

Factor out (x - y)^7 in the above expression

Expand out (x^3 - y^3) as the difference of two cubes

Combine the common factors

Rewrite the expression as:

The expression format is given as:

So, we have:

By comparison, we have:

Hence, the value of m is 8

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Step-by-step explanation:

Given the expression:

x³(x−y)⁷−y³(x−y)⁷

This can also be written as (x³-y³)(x-y)⁷

(x³-y³)(x-y)⁷=  (x-y)⁷ (x³-y³)

Expand  (x³-y³)

x³-y³ = (x-y)(x²+xy+y²)

Substitute back into the original expression:

(x-y)⁷ (x³-y³) = (x-y)⁷(x-y)(x²+xy+y²)

(x-y)⁷ (x³-y³) = (x-y)⁸(x²+xy+y²)

(x-y)⁷ (x³-y³) = (x-y)⁸(x²+y²+xy)

Comparing the result with (x−y)^m(x^2+y^2+nxy).

(x-y)⁸ = (x-y)^m

m = 8

Also:

nxy = xy

n = xy/xy

n = 1

Hence the value of m is 8

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step-by-step explanation: