Question

Verify : a(b+c) = ab + ac, where a = -1/5, b = 4/7, c = -3/2​

Answer 1

Given :

• $\sf\:a~=~\frac{-1}{5}$

• $\sf\:b~=~\frac{4}{7}$

• $\sf\:c~=~\frac{-3}{2}$

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To :

• Verify whether a ( b+c ) = ab + ac

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Concept :

For this question we need to plug the value of a, b and c in a ( b+c ) = ab + ac. Doing so and proceeding with simple calculations if we get LHS = RHS , our equation would be verified.

Hope itz clear let's proceed !~

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Solution :

$\bf\color{maroon}{⋆}$ $\sf\:a(b+c) =ab+ac$

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Plugging the given values of a, b and c

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$\sf\implies\:\frac{-1}{5}[\frac{4}{7}+(\frac{-3}{2}) ]=(\frac{-1}{5} \times \frac{4}{7}) +( \frac{-1}{5} \times \frac{-3}{2})$

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$\sf\implies\:\frac{-1}{5}[\frac{4}{7}-\frac{3}{2}]=(\frac{-1}{5} \times \frac{4}{7}) +( \frac{-1}{5} \times \frac{-3}{2})$

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• Calculating LCM of 7 and 2 in LHS = 14
• Multiplying the numbers in RHS

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$\sf\implies\:\frac{-1}{5}[\frac{(2 \times 4)-(7 \times 3)}{14}]=(\frac{-4}{35}) +(\frac{3}{10})$

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$\sf\implies\:\frac{-1}{5}[\frac{8-21}{14}]=\frac{-4}{35}+\frac{3}{10}$

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$\sf\implies\:\frac{-1}{5}[\frac{-13}{14}]=\frac{-4}{35}+\frac{3}{10}$

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$\sf\implies\:\frac{-1}{5} \times \frac{-13}{14}=\frac{-4}{35}+\frac{3}{10}$

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$\sf\implies\:\frac{13}{70}=\frac{-4}{35}+\frac{3}{10}$

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• Calculating LCM of 35 and 10 in RHS = 70

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$\sf\implies\:\frac{13}{70}=\frac{[2 \times (-4)] + (7 \times 3)}{70}$

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$\sf\implies\:\frac{13}{70}=\frac{(-8) + 21}{70}$

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$\sf\implies\:\frac{13}{70}=\frac{13}{70}$

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$\bf\implies\:LHS~=~RHS$

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Hence Verified !~

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