Question

Simplify the given expression 0.54 x 0.54 – 0.46 x 0.46=
$$\begin{gathered} \text{A}\text{. }{\left(0.54-0.46\right)}^2 \\ \text{B}\text{. }{\left(0.08\right)}^2 \\ \text{C}\text{. 0}\text{.08} \\ \text{D}\text{. 8} \end{gathered}$$

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.