Using identities, evaluate.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(i) We can write 70 as 70 + 1

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) We can write 100 as 100 - 1

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

⇒

(iii) We can write 102 as 100 + 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

⇒

(iv) We can write 998 as 1000 - 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

⇒

(v) We can write 5.2 as 5 + 0.2

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

⇒

(vi) 297× 303

We can write 297 as 300 – 3 and 303 as 300 + 3

Using Identity

In the given expression

On substituting these values in the above identity, we get

=

(vii) 78 × 82

We can write 78 as 80 – 2 and 82 as 80 + 2

Using Identity

In the given expression

On substituting these values in the above identity, we get

=

(viii) We can write 8.9 as 8 + 0.9

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

⇒

(ix) 1.05 × 9.5 = 1.05 × 0.95 × 10

We can write 1.05 as 1 + 0.05 and 0.95 × 10 as (1 – 0.05) × 10

Using Identity

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