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Find the continued product: (2x+3y)(2x-3...

Find the continued product: `(2x+3y)(2x-3y)(4x^2+9y^2)`

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To solve the problem of finding the continued product \((2x+3y)(2x-3y)(4x^2+9y^2)\), we can follow these steps: ### Step 1: Identify the first two factors We start with the first two factors: \((2x + 3y)\) and \((2x - 3y)\). ### Step 2: Apply the difference of squares identity We can use the identity \(a + b)(a - b) = a^2 - b^2\). Here, let \(a = 2x\) and \(b = 3y\). Therefore, we can rewrite the product: \[ ...
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RD SHARMA-ALGEBRAIC EXPRESSIONS AND IDENTITIES-All Questions
  1. If 4x^2+y^2=40\ a n d\ x y=6,\ find the value of 2x+ydot

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  2. Find the continued product: (x+2)(x-2)(x^2+4)

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  3. Find the continued product: (2x+3y)(2x-3y)(4x^2+9y^2)

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  4. Find the continued product: (x-1)(x+1)(x^2+1)(x^4+1)

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  5. Find the continued product: (x-1/x)(x+1/x)(x^2+1/(x^2))(x^4+1/(x^4))

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  6. Find the continued product: (x-y/5-1)(x+y/5+1)

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  7. Simplify the products: (\ x^2+x+1)(x^2-x+1)

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

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

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

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

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

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

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

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

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

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

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

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

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