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

Step-by-step explanation:

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

$29 \times 30 = (30-1) \times (30 + 1)$

$=> (30-1)(30 + 1) = 30^{2} + 30 \times (1 - 1) + (1 \times -1)$

$=> 900 + 0 - 1 = 899$

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

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

$24 \times 26 = (25-1)(25+1) = 25^{2} +25 \times (1-1) + ( 1 \times -1 )$

$=> 625 + 0 - 1 = 624$

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

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The algebraic identity used above is :-

$(x + a)(x + b) = x^{2} + (a + b)x + ab$

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