Simplify each of the following:$ 0.76 \times 0.76+2 \times 0.76 \times 0.24+0.24 \times 0.24 $

Given:

\( 0.76 \times 0.76+2 \times 0.76 \times 0.24+0.24 \times 0.24 \)

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,

\( 0.76 \times 0.76+2 \times 0.76 \times 0.24+0.24 \times 0.24 \)

The above expression is of the form $a^{2}+2 a b+b^{2}$, where $a=0.76$ and $b=0.24$.

This implies,

$0.76 \times 0.76+2 \times 0.76 \times 0.24+0.24 \times 0.24=(0.76+0.24)^{2}$

$=(1.00)^{2}$

$=1$

Hence, $0.76 \times 0.76+2 \times 0.76 \times 0.24+0.24 \times 0.24=1$. 

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Updated on: 10-Oct-2022

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