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Simplify each of the following: (7. 83 x...

Simplify each of the following: `(7. 83 xx 7. 83-1. 17 xx 1. 17)/(6. 66)`

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To simplify the expression \((7.83 \times 7.83 - 1.17 \times 1.17) / (6.66)\), we can use the algebraic identity for the difference of squares, which states that: \[ a^2 - b^2 = (a + b)(a - b) \] ### Step-by-Step Solution: ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. Simplify each of the following: 322 × 322−2 × 322 × 22+22 × 22

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  2. Simplify each of the following: 0. 76 xx 0. 76+2xx 0. 76 xx 0. 24+0. 2...

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  3. Simplify each of the following: (7. 83 xx 7. 83-1. 17 xx 1. 17)/(6. 66...

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

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

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

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

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

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

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

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

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

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  14. Simplify each of the products: (x/2-2/5)(2/5-x/2)-x^2+2x

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

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  16. Simplify each of the products: (x^3-3x^2-x)(x^2-3x+1)

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  17. Simplify each of the products: (2x^4-4x^2+1)(2x^4-4x^2-1)

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  18. Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all valu...

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  19. Write the following in expanded form: (9x+2y+z)^2 (ii) (3x+2y-z)^2

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  20. Write the following in expanded form: (x-2y-3z)^2 (ii) (-x+2y+z)^2

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