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Find the products: (i) (2x+3y)(2x-3y) ...

Find the products: (i) `(2x+3y)(2x-3y)`
(ii)`(x-1)(x+1)(x^2+1)(x^4+1)`

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Let's solve the given problems step by step. ### Part (i): Find the product `(2x + 3y)(2x - 3y)` 1. **Identify the formula**: We recognize that this expression is in the form of `(a + b)(a - b)`, which is an algebraic identity that equals `a^2 - b^2`. - Here, \( a = 2x \) and \( b = 3y \). 2. **Apply the identity**: Using the identity, we can write: ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x+1/x=6 , find x^2+1/(x^2) (ii) x^4+1/(x^4) (x+1//x)^2=6 x^2+1/...

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  2. If x^2+1/(x^2)=27 , find the values of each of the following: x+1/x (...

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  3. Find the products: (i) (2x+3y)(2x-3y) (ii)(x-1)(x+1)(x^2+1)(x^4+1)

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  4. Without calculating the actual cube find the value of (-12)^3+7^3+5^...

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  5. Expand each of the following: (i)(3x+4y)^2 (ii) (3x-4y)^2

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  6. If x-1/x=3, find the value of x^3-1/(x^3)

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  7. If 2x+3y=13 and x y=6, find the value of 8x^3+27 y^3

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  8. If a+b=10 and a^2+b^2=58 , find the value of a^3+b^3

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  9. If x+1/x=7, find the value of x^3+1/(x^3)

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  10. Simplify each of the following expressions: (i) (x+y+z)^2+(x+y/2+z/3)...

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  11. Simplify each of the following: (4x+2y)^2+(4x-2y)^2 (4x+2y)^3-(4x-...

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  12. If x+y=12 and x y=27 , find the value of x^3+y^3

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  13. 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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  14. Expand each of the following (i) (3x+4y)^2 (ii) (3x-4y)^2

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  15. Expand each of the following (i)(sqrt(2)x-3y)^2 (ii) (2x-1/(3x))^2

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  16. Expand each of the following (i)(x/2-y/3)^2 (ii) (x+5)(x-3)

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  17. Find the products: (i)(2x+3y)\ (2x-3y)

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  18. Find the products: (x-1/x)\ (x+1/x)(x^2+1/(x^2))\ (x^4+1/(x^4))

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  19. Find the products: (i) (2x+y)(2x-y)(4x^2+y^2)

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  20. Evaluate each of the following by using identities: (i)103 xx 97

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