Question

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

Answer 1

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Answer:

Jaime: yes: 29·31 = 900 -1 = 899

Raquel: 24·26 = 25^2 -1 = 624

Explanation:

The difference of squares factors as the product of the sum and difference of the roots:

a^2 -b^2 = (a -b)(a +b)

Jaime

29·31 = (30 -1)(30 +1) = 30^2 -1^2 = 900 -1 = 899

Jaime can subtract 1 from 30^2 to find 29·31

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Raquel

24·26 = (25 -1)(25 +1) = 25^2 -1^2 = 625 -1 = 624

Raquel can subtract 1^2 from 25^2 to find 24·26.