Simplify the following expression. {(375+125)^{2}-(125-375)^{2}}/{375 \times 375-125 \times 125}

SSC CGL 18 Aug 2021 Shift 2 Paper

Question : 55 of 100

Marks: +1, -0

Simplify the following expression.

\;{(375+125)^{2}-(125-375)^{2}}/{375 × 375-125 × 125}

Solution:

\;{(375+125)^{2}-(125-375)^{2}}/{375 × 375-125 × 125}

(375)^{2}+(125)^{2}+2 × 375 × 125

=\;{-[(125)^{2}+(375)^{2}-2 × 125 × 375]}/{(375)^{2}-(125)^{2}}

(375)^{2}+(125)^{2}+2 × 375 × 125

= \;\; \;{-(125)^{2}-(375)^{2}+2 × 125 × 375}/{(375-125)(375+125)}

\;{[ ∵ a^{2}-b^{2}=(a+b)(a-b)] }

= \;\; \;{4 × 125 × 375}/{250 × 500}=\;{375}/{250}=\;{3}/{2}

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