Factorize a 3-1- a 3 -A- a -1-a a 2-1- a 2B- a-1-aa2-1-a2-1C- a-1-aa2-1-q2D- a-1-aa2-1-a2-1

The correct option is D ( a + 1/a ) ( a^2 + 1/a^2 1 ) We know that a^3 + b^3 = (a + b) (a^2 + b^2 ab) So, a^3 + 1/a^3 = (a)^3 + ( 1/a )^3 = (a + 1/a) ...

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Byju's Answer

Standard VIII

Mathematics

Division of a Monomial by Another Monomial

Factorize a 3...

Question

Factorize $a^{3} + \frac{1}{a^{3}} ?$

$(a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}})$

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$(a - \frac{1}{a}) (a^{2} - \frac{1}{a^{2}})$

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$(a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} + 1)$

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$(a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} - 1)$

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Solution

The correct option is D
$(a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} - 1)$

We know that

$a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b) S o, a^{3} + \frac{1}{a^{3}} = (a)^{3} + {(\frac{1}{a})}^{3} = (a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} - a \times \frac{1}{a}) = (a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}} - 1)$

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Similar questions

Q. if

a = 6 - \sqrt{35},

find the values of the following:

(a) a^{2} + \frac{1}{a^{2}}

(b) a^{2} - \frac{1}{a^{2}}

(a) a^{4} - \frac{1}{a^{4}}

Q. If

a_{1}, a_{2}, a_{3} . . . . a_{15} \in R^{+}

and

a_{1}, a_{2}, a_{3} . . . a_{n} = 1

, then minimum value of

(1 + a_{1} + a_{1}^{2}) (1 + a_{3} + a_{3}^{2}) . . . . (1 + a_{a} + a_{a}^{2})

is equal to:_

Q. Simplify :

a (a^{2} + 1) + b (b^{2} + 1) - (a + b)

Q. Evaluate:

(a - \frac{1}{a}) (a + \frac{1}{a}) (a^{2} + \frac{1}{a^{2}}) (a^{4} + \frac{1}{a^{4}}) (a^{8} + \frac{1}{a^{8}})

Q. Simplify

a (a^{2} + a + 1) + 1

and find its value for

a = 1

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Factorize a3+1a3?

The correct option is D (a+1a)(a2+1a2−1) We know that a3+b3=(a+b)(a2+b2−ab)So,a3+1a3=(a)3+(1a)3=(a+1a)(a2+1a2−a×1a)=(a+1a)(a2+1a2−1)

Factorize $a^{3} + \frac{1}{a^{3}} ?$