Question

Simplify the following:(i) a^2 (b^2 – c^2) + b^2 (c^2 – a^2) + c^2 (a^2 – b^2)

Answer 1

Answer:

let a

2

−b

2

=x

1

;b

2

−c

2

=y

1

;c

2

−a

2

=z

1

x

1

+y

1

+z

1

=0

⇒x

1

3

+y

1

3

+z

1

3

=3x

1

y

1

z

1

=3(a

2

−b

2

)(b

2

−c

2

)(c

2

−a

2

)

let a−b=x

2

;b−c=y

2

;c−a=z

2

x

2

+y

2

+z

2

=0

⇒x

2

3

+y

2

3

+z

2

3

=3x

2

y

2

z

2

=3(a−b)(b−c)(c−a)

So,

x

2

3

+y

2

3

+z

2

3

x

1

3

+y

1

3

+z

1

3

=(a+b)(b+c)(c+a)

Step-by-step explanation:

Mark me as brainliest if it's helpful..Thank you...