# Simplify the given expression 0.54 x 0.54 – 0.46 x 0.46=

$

{\text{A}}{\text{. }}{\left( {0.54 - 0.46} \right)^2} \\

{\text{B}}{\text{. }}{\left( {0.08} \right)^2} \\

{\text{C}}{\text{. 0}}{\text{.08}} \\

{\text{D}}{\text{. 8}} \\

$

Last updated date: 24th Mar 2023

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Answer

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Hint – To simplify the equation given in the question we use the algebraic formula (${{\text{a}}^2}$– ${{\text{b}}^2}$) and solve for answer.

Complete step-by-step answer:

Given Data,

0.54x0.54 – 0.46x0.46 = $\left( {{{0.54}^2} - {{0.46}^2}} \right)$

Now, Let a = 0.54 and b = 0.46

⟹$\left( {{{0.54}^2} - {{0.46}^2}} \right)$ = (${{\text{a}}^2}$ – ${{\text{b}}^2}$)

= (a + b) × (a – b)

= (0.54 + 0.46) × (0.54 – 0.46)

= 1x 0.08

= 0.08

Hence Option C is the correct answer.

Note – In order to solve this type of questions the key is to identify if the given equation fits into a known algebraic formula, if not we reduce it in such a way that it transforms into a known formula. Basic knowledge in algebraic formulae is required.

Complete step-by-step answer:

Given Data,

0.54x0.54 – 0.46x0.46 = $\left( {{{0.54}^2} - {{0.46}^2}} \right)$

Now, Let a = 0.54 and b = 0.46

⟹$\left( {{{0.54}^2} - {{0.46}^2}} \right)$ = (${{\text{a}}^2}$ – ${{\text{b}}^2}$)

= (a + b) × (a – b)

= (0.54 + 0.46) × (0.54 – 0.46)

= 1x 0.08

= 0.08

Hence Option C is the correct answer.

Note – In order to solve this type of questions the key is to identify if the given equation fits into a known algebraic formula, if not we reduce it in such a way that it transforms into a known formula. Basic knowledge in algebraic formulae is required.

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