Answer:
(a) 4a³
Explanation:
You want the a³ term in the product of the two given polynomials.
Product
The bottom line in the "vertical method" multiplication table shown is the sum of the partial-product expressions in the column above the bottom line:
B = 12a³ -6a³ -2a³ = (12 -6 -2)a³
B = 4a³
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Additional comment
The value of A can be found a couple of ways.
You can find the partial product of the 1st-degree terms in each of the polynomials: (-2a)(-2a) = 4a².
Or you can find the value of A that is required to give the bottom-line result that is shown:
9a² +A +a² = 14a²
A = 14a² -10a²
A = 4a²
Multiplying polynomials is substantially equivalent to multiplying multi-digit numbers. The difference is that there is no carry from one column to the next when you compute the partial products or the final sum.