Question

drag the operator to the correct location on the image.

which operation results in a binomial?

\\((3y^6 + 4) \box (9y^{12} - 12y^6 + 16)\\)

\\(\cdot\\) \\(-\\) \\(+\\)

Explanation:

Analyze the algebraic structure

$$
LATEXBLOCK0
$$

Evaluate multiplication using sum of cubes identity

$$ (a + b)(a^2 - ab + b^2) = a^3 + b^3 $$

$$ (3y^6 + 4)(9y^{12} - 12y^6 + 16) = (3y^6)^3 + 4^3 = 27y^{18} + 64 $$

Verify the resulting polynomial type

$$ 27y^{18} + 64 \text{ is a binomial (two terms).} $$

Answer:

Which operation results in a binomial?

\((3y^6 + 4)\) <blank>\(\cdot\)</blank> \((9y^{12} - 12y^6 + 16)\)