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given that m=5 and n=50, which is greater, (m+n)(m-n) or 100? explain.

Sagot :

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(5+50)(5-50)=25+250-250-2500=-2475, 100 is greater since -2475 is negative in value while 100 is positive which means it is greater since positive integers r always greater than negative
Substitute the values of m and n to the expression:

Option 1:
(m + n) (m - n)
(5 + 50) (5 - 50) = (55) (-45) = - 2475

Option 2:
Sum and Difference of two binomials
(m + n) (m - n) = m² - n²

(5)² - (50)² = (25) - (2,500)  = - 2,475

100 > -2,475

100 is greater than -2,475 because 100 is a positive integer, while - 2,475 is a negative integer. Any positive integer is greater than a negative integer.

In the special products "the sum and difference of two binomials", its product is always less than 100 or less than 0 (in general) if  the first term of the binomial is less than the second term.  Naturally, the difference of the same binomial yields a negative integer.  Multiply a negative integer by a positive integer, the result is negative.  Any negative integer is less than 0, 1, 2, 3, ... (positive integers)