Step-by-step explanation:
If Jaime knows that 30² = 900 , he can use it in finding 29×31. Lets see how :-
[tex]29 \times 30 = (30-1) \times (30 + 1)[/tex]
[tex]=> (30-1)(30 + 1) = 30^{2} + 30 \times (1 - 1) + (1 \times -1)[/tex]
[tex]=> 900 + 0 - 1 = 899[/tex]
Hence , we can find the 29×31 by using 30².
Similarly , Raquel can find 24×26 by using 25². Lets see how :-
[tex]24 \times 26 = (25-1)(25+1) = 25^{2} +25 \times (1-1) + ( 1 \times -1 )[/tex]
[tex]=> 625 + 0 - 1 = 624[/tex]
Hence , we can find the ×26 by using 25².
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The algebraic identity used above is :-
[tex](x + a)(x + b) = x^{2} + (a + b)x + ab[/tex]
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