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Evaluate ${(49)}^{2}$ using the identity ${(a - b)}^{2}$ = $a^{2} - 2 ab + b^{2}$ .The final value is:

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2401

2501

2801

2001

answer is A.

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Detailed Solution

Concept: Write 49 as 50 - 1 to evaluate

{(49)}^{2}

using the identity

{(a - b)}^{2}

a^{2} - 2 ab + b^{2}

then compare and replace the values in the supplied identity.
We can write

{(49)}^{2}

{(50 - 1)}^{2}

Take a = 50 and b = 1, and replace them in the expansion of the formula for calculating the value in mathematical form.

{(a - b)}^{2}

a^{2} - 2 ab + b^{2}

{(50 - 1)}^{2}

50^{2}

+12−2(50)(1)
The value of

50^{2}

is 2500

{(50 - 1)}^{2} =

2500 + 1−100

{(50 - 1)}^{2}

= 2501−100

49^{2} = 2401

So, the value of

{(49)}^{2}

using the identity

{(a - b)}^{2}

a^{2} - 2 ab + b^{2}

is 2401.
Hence, option 1 is correct.

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