Question

find the product of (y-1/y)(y+1/y)and (y^2+1/y^2)

Answer 1

Step-by-step explanation:

Hey Mate,

Your answer_______

( Y-1 ) ( Y+1 )

Y to the power 2 -- 1

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# jai hind #

Answer 2

Answer:

Given:

$\left(y-\dfrac{1}{y}\right) \left(y+\dfrac{1}{y}\right) \left( y^2 + \dfrac{1}{y^2}\right)$

Solution:

$\implies \left(y-\dfrac{1}{y}\right) \left(y+\dfrac{1}{y}\right) \left( y^2 + \dfrac{1}{y^2}\right)$

$\implies \left(y^2 - \dfrac{1}{y^2}\right)\left(y^2 + \dfrac{1}{y^2}\right)$

$\implies \left(y^4 - \dfrac{1}{y^4}\right)$

Identity used :

$\boxed{(a+b)(a-b) = a^2 - b^2}$

Additional information:

$\begin{lgathered}\boxed{\begin{array}{l}Some \ algebric \ identities : \\\\(a+b)^2 = a^2 + b^2 + 2ab \\(a-b)^2 = a^2 + b^2 - 2ab \\(a+b)(a-b) = a^2 - b^2 \\(x+a)(x+b) = x^2 + (a+b)x + ab \\(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \\(a+b+c)^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - 2ab - 2bc - 2ca)\\(a+b+c)^3 = a^3 + b^3 + c^3 + 3(a+b)(b+c)(c+a)</p><p>\end{array}}\end{lgathered}$