The two binomials can be written as (x - a)(x + a), for any constant a.
Proof:
Expand using FOIL:
(x - a)(x + a) = x2 + xa - xa - a2
Group:
(x - a)(x + a) = x2 - a2
x2 - a2 is a difference of squares. Thus, the product of (x - a) and (x + a) is a difference of squares.
The proposition in the question is simply not true so there can be no answer!For example, if given the integer 6:there are no two perfect squares whose sum is 6,there are no two perfect squares whose difference is 6,there are no two perfect squares whose product is 6,there are no two perfect squares whose quotient is 6.
-12
They are: 7 and 5 because 49-25 = 24
Two binomials whose sum is a binomial can be expressed as (a + b) and (c - b), where (a) and (c) are constants, and (b) is a common variable. When you add these two binomials, the (b) terms cancel out, resulting in the binomial (a + c). For example, if you have (3x + 2) and (5 - 2), their sum is (3x + 5), which is a binomial.
A cube.
The proposition in the question is simply not true so there can be no answer!For example, if given the integer 6:there are no two perfect squares whose sum is 6,there are no two perfect squares whose difference is 6,there are no two perfect squares whose product is 6,there are no two perfect squares whose quotient is 6.
the two consecutive positive integers whose product is 380 19 20
Two primes whose squares have a difference of 42 are 7and 11.
-76 and 76 whose product is -5776.
4 and 7 -4 and -7
11,8
11
-12
They are: 7 and 5 because 49-25 = 24
-5 * 5 = -25
17 and 53
-3 and 6.