Question

Evaluate 108 × 97 using identity.

Answer 1

SOLUTION

TO DETERMINE

Evaluate 108 × 97 using identity.

EVALUATION

We are aware of the identity that

$\displaystyle\sf{ ab = { \bigg( \frac{a + b}{2} \bigg)}^{2} -{ \bigg( \frac{a - b}{2} \bigg)}^{2} }$

EVALUATION

We have to find the value of 108 × 97

Let a = 108 & b = 97

$\displaystyle\sf{ 108 \times 97 }$

$\displaystyle\sf{ = { \bigg( \frac{108 + 97}{2} \bigg)}^{2} -{ \bigg( \frac{108 - 97}{2} \bigg)}^{2} }$

$\displaystyle\sf{ = { \bigg( \frac{205}{2} \bigg)}^{2} -{ \bigg( \frac{11}{2} \bigg)}^{2} }$

$\displaystyle\sf{ = \frac{42025 - 121}{4} }$

$\displaystyle\sf{ = \frac{41904}{4} }$

$\displaystyle\sf{ = 10476}$

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Answer 2

Step-by-step explanation:

$42025−121</p><p> </p><p> </p><p></p><p>\displaystyle\sf{ = \frac{41904}{4} }= </p><p>4</p><p>41904</p><p> </p><p> </p><p></p><p>\displaystyle\sf{ = 10476}=10476$