Question

Factorize-
$a ^ { 4 } ( b - c ) + b ^ { 4 } ( c - a ) + c ^ { 4 } ( a - b )$
Correct answer will be marked brainliest​

Answer 1

Answer:

The given equation is a

4

(b

2

−c

2

)+b

4

(c

2

−a

2

)+c

4

(a

2

−b

2

)

We can write the above equation as

a

4

(b

2

−c

2

)−b

4

(b

2

−c

2

+a

2

−b

2

)+c

4

(a

2

−b

2

)

=a

4

(b

2

−c

2

)−b

4

(b

2

−c

2

)−b

4

(a

2

−b

2

)+c

4

(a

2

−b

2

)

=(b

2

−c

2

)(a

4

−b

4

)−(a

2

−b

2

)(b

4

−c

4

)

=(b

2

−c

2

)(a

2

−b

2

)(a

2

+b

2

)−(a

2

−b

2

)(b

2

−c

2

)(b

2

+c

2

)

=(b

2

−c

2

)(a

2

−b

2

)(a

2

+b

2

−b

2

−c

2

)

=(b

2

−c

2

)(a

2

−b

2

)(a

2

−c

2

)

=−(b

2

−c

2

)(a

2

−b

2

)(c

2

−a

2

)

=−(b+c)(b−c)(a+b)(a−b)(c+a)(c−a)