Expand the algebraic expression a1-2a1-2 - a-1-2

A^1/2(a^1/2 + a^ 1/2) = a^1/2· a^1/2 + nbsp;a^1/2· nbsp; a^ 1/2 nbsp; Using Distributive property of multiplication = nbsp;a^1/2 + 1/2 nbsp; + nbsp; ...

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Standard VIII

Mathematics

Operations on Exponents in Algebraic Expansions

Expand the al...

Question

Expand the algebraic expression $a^{\frac{1}{2}} (a^{\frac{1}{2}} + a^{\frac{- 1}{2}})$

a

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a + 1

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a + 2

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a + 3

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Solution

The correct option is B $a + 1$
$a^{\frac{1}{2}} (a^{\frac{1}{2}} + a^{\frac{- 1}{2}}) = a^{\frac{1}{2}} \cdot a^{\frac{1}{2}} + a^{\frac{1}{2}} \cdot a^{\frac{- 1}{2}}$
Using Distributive property of multiplication
$= a^{\frac{1}{2} + \frac{1}{2}} + a^{\frac{1}{2} + (\frac{- 1}{2})}$
$= a^{1} + a^{0}$
$= a + 1 (a \neq 0)$

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Expand the algebraic expression a12(a12+a−12)

The correct option is B a+1a12(a12+a−12)=a12⋅a12+a12⋅a−12 Using Distributive property of multiplication =a12+12+a12+(−12) =a1+a0 =a+1 (a≠0)

Expand the algebraic expression $a^{\frac{1}{2}} (a^{\frac{1}{2}} + a^{\frac{- 1}{2}})$