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Evaluate each of the following using ide...

Evaluate each of the following using identities: `(a^2b-b^2a)^2` (ii) `(a-0. 1)(a+0. 1)`

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given (i)`(a^2b-b^2a)^2`
`=(a^2b)^2+(b^2a)^2-2xxa^2bxxb^2a`
since `(x-y)^2=x^2+y^2-2xy`
`=a^4b^2+b^4a^2-2a^3b^3`
(ii) `(a-0. 1)(a+0. 1)`
`=a^2-(0.1)^2`
(since `(x+y)(x-y)=x^2-y^2`)
`=a^2-0.01`
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
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  8. Simplify each of the following: 322 × 322−2 × 322 × 22+22 × 22

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  11. If x+1/x=11 , find the value of x^2+1/(x^2)

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  12. If x-1/x= -1, find the value of x^2+1/(x^2)

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  13. If x+1/x=sqrt(5) , find the values of x^2+1/(x^2) and x^4+1/(x^4)

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  14. If x^2+1/(x^2)=66 , find the value of x-1/x

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  15. If x^2+1/(x^2)=79 , find the value of x+1/x

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  16. If 9x^2+25 y^2=181\ \ a n d\ x y\ =\ -6, find the value of 3x+5y

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  17. If 2x+3y=8 and x y=2 , find the value of 4x^2+9y^2

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  18. If 3x-7y=10 and x y=-1, find the value of 9x^2+49 y^2

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  19. Simplify each of the products: (1/2a-3b)(1/2a+3b)(1/4a^2+9b^2)

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  20. Simplify each of the products: (m+n/7)^3 (m-n/7)

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