drag the operator to the correct location on the image. which operation results in a binomial? (3y^6 + 4)…
drag the operator to the correct location on the image. which operation results in a binomial? (3y^6 + 4) (9y^12 - 12y^6 + 16)
Answer
Answer:
×
Explanation:
Step1: Recall the sum - of - cubes formula
The sum - of - cubes formula is $(a + b)(a^{2}-ab + b^{2})=a^{3}+b^{3}$. Here, $a = 3y^{6}$ and $b = 4$. So, $(3y^{6}+4)(9y^{12}-12y^{6}+16)=(3y^{6})^{3}+4^{3}=27y^{18}+64$, which is a binomial.
Step2: Check other operations
If we use subtraction: $(3y^{6}+4)-(9y^{12}-12y^{6}+16)=-9y^{12}+15y^{6}-12$, which is a trinomial. If we use division: $\frac{3y^{6}+4}{9y^{12}-12y^{6}+16}$ is a rational function, not a binomial.