Question

Factorise x⁴(y-z)+y⁴(x-x)+z⁴(x-y)​

Answer 1

Answer:

- (x - y)(y - z)(z - x)(x² + y² + z² + xy + yz + zx)

Step-by-step explanation:

x⁴(y - z) + y⁴(z - x) + z⁴(x - y)​

= x⁴y - x⁴z + y⁴z - y⁴x + z⁴x - z⁴y

= x⁴(y - z) - x(y⁴ - z⁴) + yz(y³ - z³)

= x⁴(y - z) - x(y - z​)(y + z)(y² + z²) + yz(y - z)(y² + yz + z²)

= (y - z) [x⁴ - xy³ - xyz²- xy²z - xz³ + y³z + y²z² + yz³)

= (y - z) [y³(z - x) + y²(z² - xz) + (y - x)(z³ - x³)]

= (y - z)(z - x) [y³ + y²z + (y - x)(z² + xz + x²)]

= (y - z)(z - x) [y³ + y²z + yz² + xyz + x²y - xz² - x²z - x³]

= (y - z)(z - x) [z²(y - x) + z(y² - x²) + (y³ - x³)]

= (y - z)(z - x)(y - x) [z² + zy + zx + y² + xy + x²]

= - (x - y)(y - z)(z - x)(x² + y² + z² + xy + yz + zx)

Hope this helps! :)

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Answer 2

Answer:

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