Simplify each of the following:
$ 175 \times 175+2 \times 175 \times 25+25 \times 25 $

Given:

\( 175 \times 175+2 \times 175 \times 25+25 \times 25 \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$175 \times 175+2 \times 175 \times 25+25 \times 25$

The above expression is of the form $a^{2}+2 a b+b^{2}$ where, $a=175$ and $b=25$.

This implies,

$175 \times 175+2 \times 175 \times 25+25 \times 25=(175+25)^{2}$

$=(200)^{2}$

$=40000$

Hence, $175 \times 175+2 \times 175 \times 25+25 \times 25=40000$.

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Updated on: 10-Oct-2022

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