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Square

A square can be taken over several terms.

 


Two terms

To solve a square with two terms you should calculate this term-by-term

(a + b)2

and that gives

(a + b) (a + b) = a + b + a + b

so

(a + b)2 =  a2 + 2ab + b2

It's a binomial formula that is often used to simplify calculations. We check this with regular numbers

(2 + 3)2 = (2 + 3) (2 + 3) = 2·2 + 2·3 + 3·2 + 3·3  = 25

and this result is of course correct, as

(2 + 3)2 = (5)2 = 25

 


Three terms

To solve a square with three terms you must also work from left to right

(2 + 3 + 4)2 = (2 + 3 + 4) (2 + 4) = 2·2 + 2·3 + 2·4 + 3·2 + 3·3 + 3·4 + 4·2 + 4·3 + 4·4 = 81

and that result is of course correct, as

(2 + 3 + 4)2 = (9)2 = 81

 


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