Question

Evaluate 95 × 105 by expressing it as a difference of two squares

Answer 1

( 95 ) ( 105 )


( 100 - 5 ) ( 100 + 5 )

( 100 )^2 - ( 5 )^2

10000 - 25

9975


$.$




Hence, value of ( 95 × 105 ) is 9975 by using the formula ( a + b ) ( a - b ) = a^2 - b^2

Answer 2

Hey there!

So, We are asked to evaluate 95 * 105 by expressing it as difference of two squares

Let the two squares whose difference would be equal to 95 * 105 are a² , b²

So, a² - b² = ( 95 * 105 )

( a + b) ( a - b) = 95 * 105

So , We have to express 95 & 105 as a+b and a-b and proceed solving them further.

95 * 105

= ( 100 - 5 ) ( 100 + 5 )

Use the identity a² - b² = ( a + b) ( a - b)

= 100² - 5²

= 10,000- 25

= 9975

So , The product of 95 and 105 is 9975