Real Life Use of Algebraic Identities
Suppose, your friends Tanmay and Swati have some money.
They want to buy coloured paper to cover their notebooks.
They go to a stationery shop in the nearby market.
The stationery shop owner told them that he sells square coloured paper at the rate of Rs
$1$
for
$1$
decimeter side length.
They both wanted to buy separate sheets of paper
But the shopkeeper told them that it would be wise to buy a single sheet of paper.
They didnâ€™t understand his point and asked for explanation.
Letâ€™s help them understand the explanation.
Suppose Tanmay has Rs
$7$
and Swati have Rs
$3$
Now, letâ€™s find the total area of the square sheet if they buy separately.
Now, letâ€™s find the area of the single sheet if they buy together.
Hence we can see that it is wise to buy a single sheet rather than buying separately because
$100dm_{2}$
is for sure profitable than
$58dm_{2}$
.
Letâ€™s understand the mathematics behind it.
Suppose, Tanmay and Swati have Rs
$a$
and Rs
$b$
respectively.
Now. if they buy two separate sheets, total area of the sheets is given as
And if they buy a single sheet together, area of the sheet is given as
So we have area of the single sheet as,
So area of the single sheet is greater than the total area of separate sheets.
This equation obtained above is a standard identity
In a similar manner we have four another standard identities.
Letâ€™s discuss how to apply these identities in questions.
Suppose we have to expand the above expression.
We know that the first algebraic identity is
So letâ€™s us compare the above expression with the first identity.
Applying the first identity we can expand the expression as,
Now, suppose we have to expand the above expression.
We know that the second algebraic identity is
Comparing the given expression with the second identity, we get
So we can expand the expression in the shown manner.
Now, suppose we have to expand the following expression.
We know that the third algebraic identity is given by,
Comparing the above expression with the third identity we get,
With the help of third identity, we can expand the given expression as,
Now, suppose we have to find the expansion of the above expression.
We know that the fourth algebraic identity is given as,
When the expression is compared with the fourth identity, we get
So the expression can be expanded as,
Revision
The four standard algebraic identities are given above.
The End