Evaluate 492 using the identity a-b2=a2-2ab+b2.The final value is:

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

1. A
2401
2. B
2501
3. C
2801
4. D
2001

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Concept: Write 49 as 50 - 1 to evaluate ${\left(49\right)}^{2}$ using the identity ${\left(a-b\right)}^{2}$= then compare and replace the values in the supplied identity.
We can write ${\left(49\right)}^{2}$as ${\left(50-1\right)}^{2}$
Take a = 50 and b = 1, and replace them in the expansion of the formula for calculating the value in mathematical form.
${\left(a-b\right)}^{2}$=
${\left(50-1\right)}^{2}$= ${50}^{2}$+12−2(50)(1)
The value of
${50}^{2}$ is 2500
${\left(50-1\right)}^{2}=$ 2500 + 1−100
${\left(50-1\right)}^{2}$= 2501−100
${49}^{2}=2401$
So, the value of ${\left(49\right)}^{2}$using the identity ${\left(a-b\right)}^{2}$= ${a}^{2}-2\mathit{ab}+{b}^{2}$ is 2401.
Hence, option 1 is correct.

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)