Question

Jaime knows that 30² is 900. He wonders if knowing 30² can help him find 29x31. Raquel knows what 25² equals. How can she use the knowledge to find 24x26?

Thanks

Answer 1

Explanation:

If Jaime knows that 30² = 900 , he can use it in finding 29×31. Lets see how :-

`29 * 30 = (30-1) * (30 + 1)`

`=> (30-1)(30 + 1) = 30^(2) + 30 * (1 - 1) + (1 * -1)`

`=> 900 + 0 - 1 = 899`

Hence , we can find the 29×31 by using 30².

Similarly , Raquel can find 24×26 by using 25². Lets see how :-

`24 * 26 = (25-1)(25+1) = 25^(2) +25 * (1-1) + ( 1 * -1 )`

`=> 625 + 0 - 1 = 624`

Hence , we can find the ×26 by using 25².

__________________________________________________

The algebraic identity used above is :-

`(x + a)(x + b) = x^(2) + (a + b)x + ab`

__________________________________________________