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Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c...

Prove that: `2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2`

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Given:
`=> 2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2`
Solve R.H.S. equation
`=> (a-b)^2+(b-c)^2+(c-a)^2`
Using the identity :
`(a-b)^2=a^2+b^2-2ab`
...
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RD SHARMA-ALGEBRAIC EXPRESSIONS AND IDENTITIES-All Questions
  1. Simplify the products: (\ x^2+x+1)(x^2-x+1)

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  2. Simplify the products: (x^2+2x+2)(x^2-2x+2)

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  3. Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2

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  4. If a^2+b^2+c^2-ab-bc-ca=0, prove that a=b=c

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  5. Using the formulae for squaring a binomial, evaluate the following :...

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  6. Simplify the following by using (a+b)(a-b)=a^2-b^2 (i) 68 xx 72 (ii)...

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  7. Find the value of x , if 6x=23^2-17^2

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  8. Find the value of x , if 4x=98^2-88^2

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  9. Find the value of x , if 25 x=536^2-136^2

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  10. What must be added to 9x^2-24 x+10 to make it a whole square?

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  11. Write the following squares of binomials as trinomials: (i) (x+2)^2 ...

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  12. Write the following squares of binomials as trinomials: (i)(x+(x^2)...

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  13. Write the following squares of binomials as trinomials: (i) ((3a)/2-...

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  14. Find the product of the following binomials; (i)(2x+y)(2x+y) (ii) (...

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  15. Find the product of the following binomials; (i)(a^2+b c)(a^2-b c) ...

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  16. Find the product of the following binomials; (2x+3/y)(2x-3/y) (ii)...

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  17. Find the product of the following binomials; (i)(x^4+2/(x^2))(x^4-2/...

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  18. Using the formula for squaring a binomial , evaluate the following: ...

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  19. Using the formula for squaring a binomial , evaluate the following: ...

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  20. Simplify the following using the formula: (a-b)(a+b)=a^2-b^2: (i)(82...

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