Answer :

(i) Using Identity (a - b) ^{2} = a^{2} - 2ab + b^{2}

In the given expression a =

On substituting these values in the above identity, we get

= a^{4} - 2a^{2}b^{2} + b^{4}

(ii)

Using Identity a^{2} - b^{2} = (a + b)(a - b)

In the given expression a =

On substituting these values in the above identity, we get

(iii)

Using Identity (a - b)^{2} = a^{2} - 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

Using Identity (a + b) ^{2} = a^{2} + 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(ii)

On Adding equations (i) and (ii), we get

(iv)

Using Identity (a + b) ^{2} = a^{2} + 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

Using Identity (a + b) ^{2} = a^{2} + 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(ii)

On Adding equations (i) and (ii), we get

(v)

Using Identity (a - b) ^{2} = a^{2} - 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

Using Identity (a - b) ^{2} = a^{2} - 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

On Subtracting equations (ii) from (i), we get

(vi)

Using Identity (a + b)^{2} = a^{2} + 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

On Subtracting from (i), we get

(vii) (m^{2} - n^{2}m)^{2} + 2m^{3}n^{2}

Using Identity (a - b) ^{2} = a^{2} - 2ab + b^{2} for finding the value of

In the given expression a =

On substituting these values in the above identity, we get

⇒ ………………………………………………..(i)

On adding to equation (i), we get

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