Question
Simplify the following:
$175 \times 175+2 \times 175 \times 25+25 \times 25$
$175 \times 175+2 \times 175 \times 25+25 \times 25$
✓
Answer
We have,
$175 \times 175+2 \times 175 \times 25+25 \times 25=(175)^2+2(175)(25)+(25)^2$
$=(175+25)^2\left[a^2+b^2+2 a b=(a+b)^2\right]$
$=(200)^2[\text { Where } a=175 \text { and } b=25]$
$=40000$
Therefore, $175 \times 175+2 \times 175 \times 25+25 \times 25=40000$.
$175 \times 175+2 \times 175 \times 25+25 \times 25=(175)^2+2(175)(25)+(25)^2$
$=(175+25)^2\left[a^2+b^2+2 a b=(a+b)^2\right]$
$=(200)^2[\text { Where } a=175 \text { and } b=25]$
$=40000$
Therefore, $175 \times 175+2 \times 175 \times 25+25 \times 25=40000$.
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