Find each of the following products- x4-1-x4 - x-1-x

( x^4+1/x^4 )× ( x+1/x ) =x^4 ( x+1/x )×1/x^4 ( x+1/x ) =x^4× x+x^4×1/x+1/x^4× x+1/x^4×1/x =x^5+x^3+1/x^3+1/x^5 ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Any Polynomial

Find each of ...

Question

Find each of the following products:

$(x^{4} + \frac{1}{x^{4}}) \times (x + \frac{1}{x})$

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Solution

$(x^{4} + \frac{1}{x^{4}}) \times (x + \frac{1}{x}) = x^{4} (x + \frac{1}{x}) \times \frac{1}{x^{4}} (x + \frac{1}{x}) = x^{4} \times x + x^{4} \times \frac{1}{x} + \frac{1}{x^{4}} \times x + \frac{1}{x^{4}} \times \frac{1}{x} = x^{5} + x^{3} + \frac{1}{x^{3}} + \frac{1}{x^{5}}$

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Similar questions

Q. If

x^{4} + \frac{1}{x^{4}} = 6239

, find

x + \frac{1}{x}

Q. If

x - \frac{1}{x} = 2

, find

x^{4} + \frac{1}{x^{4}}

Find in each case, the remainder when
(i) $x^{4} - 3 x^{2} + 2 x + 1$ is divided by x - 1
(ii) $x^{3} + 3 x^{2} - 12 x + 4 i s d i v i d e d b y x - 2$
(iii) $x^{4} + 1 i s d i v i d e d b y x + 1.$

Q. If

x + \frac{1}{x} = 3

, find the value of

x^{4} + \frac{1}{x^{4}}

Q. If

x + \frac{1}{x} = 3

, Find the value of

x^{4} + \frac{1}{x^{4}}

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Find each of the following products: (x4+1x4)×(x+1x)

(x4+1x4)×(x+1x)=x4(x+1x)×1x4(x+1x)=x4×x+x4×1x+1x4×x+1x4×1x=x5+x3+1x3+1x5

Find each of the following products:

$(x^{4} + \frac{1}{x^{4}}) \times (x + \frac{1}{x})$

$(x^{4} + \frac{1}{x^{4}}) \times (x + \frac{1}{x}) = x^{4} (x + \frac{1}{x}) \times \frac{1}{x^{4}} (x + \frac{1}{x}) = x^{4} \times x + x^{4} \times \frac{1}{x} + \frac{1}{x^{4}} \times x + \frac{1}{x^{4}} \times \frac{1}{x} = x^{5} + x^{3} + \frac{1}{x^{3}} + \frac{1}{x^{5}}$