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Show that : (i) (3x+7)^2-84 x=(3x-7)^2...

Show that :
(i) `(3x+7)^2-84 x=(3x-7)^2`
(ii) `(9a-5b)^2+180 a b=(9a+5b)^2`
(iii) `((4m)/3-(3n)/4)^2+2m n=(16 m^2)/9+(9n^2)/(16)`

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Given:
`(i) (3x+7)^2-84 x=(3x-7)^2`
`=> (9x^2+49+42x-84x)=(9x^2+49-42x)^2`
`=> (9x^2+49-42x)=(9x^2+49-42x)^2`
`=> LHS=RHS`
`(ii) (9a-5b)^2+180 a b=(9a+5b)^2`
`=> (81a^2+25b^2-90ab+180ab)=(81a^2+25b^2+90ab)`
`=> (81a^2+25b^2+90ab)=(81a^2+25b^2+90ab`
...
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RD SHARMA-ALGEBRAIC EXPRESSIONS AND IDENTITIES-All Questions
  1. If x-y=7\ a n d\ x y=9, find the value of x^2+y^2

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  2. If 3x+5y=11 and xy=2, find the value of 9x^2+25 y^2

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  3. Find the values of the following expressions: (i) 16 x^2+24+9 , when...

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  4. If x+1/x=9. find the value of x^4+1/(x^4)dot

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  5. If x+1/x=12 , find the value of x-1/xdot

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  6. If 2x+3y=14 a n d 2x-3y=2, find the value of x y [Hint use (2x+3y)^2-...

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  7. If x^2+y^2=29 a n d x y=2, find the value of (i)x+y (ii) x-y

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  8. What must be added to each of the following expressions to make it a...

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  9. Simplify: (i) (x-y)(x+y)x^2+y^2) (x^4+y^4) (ii) (2x-1) (2x+1)(4x^2...

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  10. Simplify: (m^2-n^2m)^2+2m^3n^2

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  11. Show that : (i) (3x+7)^2-84 x=(3x-7)^2 (ii) (9a-5b)^2+180 a b=(9a+...

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  12. Show that : (i) (4p q+3q)^2-(4q p-3q)^2=48 p q^2 (ii) (a-b)(a+b)+(...

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  13. Find the following products: (i) (x+2)(x+3) (ii)(x+7)(x-2) (iii...

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  14. Evaluate the following : (i)107 xx 103 (ii) 56xx 48 (iii) 95 xx97

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  15. Find the following products: (i)(x+4)(x+7) (ii) (x-11)(x+4) (i...

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  16. Find the following products: (i)(y^2-4)(y^2-3) (ii) (x+4/3)(x+3/4) ...

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  17. Find the following products: (i)z^2+2)(z^2-3) (ii) (3x-4y)(2x-4y) ...

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  18. Find the following products: (i)(z+3/4)(z+4/3) (ii) (x^2+4)(x^2+9) ...

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  19. Evaluate the following : (i)102 xx 106 (ii) 109 xx 107 (iii)35 xx...

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  20. Evaluate the following : (i)103 xx 96 (ii) 34 xx 36 (iii) 994 xx ...

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