Respuesta :

abidemiokin

Answer:

m = 8

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

MrRoyal

The value of m is 8

The expression is given as:

[tex]x^3(x-y)^7-y^3(x-y)^7[/tex]

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

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x^3 - y^3)(x -y)^7[/tex]

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

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x-y)(x\²+xy+y\²)(x -y)^7[/tex]

Combine the common factors

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x\²+xy+y\²)(x -y)^8[/tex]

Rewrite the expression as:

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x -y)^8(x\²+xy+y\²)[/tex]

The expression format is given as:

[tex](x-y)^m(x^2+y2^+nxy)[/tex]

So, we have:

[tex](x-y)^m(x^2+y2^+nxy) = (x -y)^8(x\²+xy+y\²)[/tex]

By comparison, we have:

[tex]m = 8[/tex]

Hence, the value of m is 8

Read more about expressions at:

https://brainly.com/question/4344214

Otras preguntas