Question

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}} \\
$

Answer 1

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.