Question

Which operation results in a binomial? (3y ^ 6 + 4) (9y ^ 12 - 12y ^ 6 + 16)

Answer 1

Step-by-step explanation:

Given the expression, $(3y ^ 6 + 4) (9y ^ {12} - 12y ^ 6 + 16)$, we want to know which sign placed in between the two polynomial will produce a binomial.

Using a plus (+) sign to check:

$= (3y ^ 6 + 4) + (9y ^ {12} - 12y ^ 6 + 16)\\= (3y ^ 6 + 4) + (9y ^ {12} - 12y ^ 6 + 16)\\collect \ like \ terms\\= 9y^{12} +3y^6 - 12y^6 + 16+ 4\\= 9y^{12} - 9y^6 + 20$

From the gotten value, it can be seen that the resulting answer produces 3 terms, showing that it results in a trinomial instead of binomial.

Using a plus (-) sign to check:

$= (3y ^ 6 + 4) - (9y ^ {12} - 12y ^ 6 + 16)\\= 3y ^ 6 + 4 - 9y ^ {12} + 12y ^ 6 - 16\\collect \ like \ terms\\= -9y^{12} +3y^6 +12y^6 + 4-16\\= -9y^{12} +15y^6 -12$

From the gotten value, it can be seen that the resulting answer produces 3 terms, showing that it results in a trinomial instead of binomial.

Hence none of the operations given results in a binomial