Simplify each of the following:$ 322 \times 322-2 \times 322 \times 22+22 \times 22 $

Given:

\( 322 \times 322-2 \times 322 \times 22+22 \times 22 \)

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,

$322 \times 322-2 \times 322 \times 22+22 \times 22$

The above expression is of the form $a^{2}-2 a b+b^{2}$, where $a=322$ and $b=22$.

This implies,

$322 \times 322-2 \times 322 \times 22+22 \times 22=(322-22)^{2}$

$=(300)^{2}$

$=90000$

Hence, $322 \times 322-2 \times 322 \times 22+22 \times 22=90000$.

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Updated on: 10-Oct-2022

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