Answer:
[tex]A=4a^2\\ \\B=4a^3[/tex]
Step-by-step explanation:
When you multiply two ploynomials using vertical method, you multiply the first polynomial by each term of the second polynomial and write the result of multiplication under the first horizontal line as shown on the diagram.
1. Multiply [tex]4a^3+3a^2-2a+1[/tex] by 3:
[tex](4a^3+3a^2-2a+1)\times 3=12a^3+9a^2-6a+3[/tex]
2. Multiply [tex]4a^3+3a^2-2a+1[/tex] by [tex]-2a:[/tex]
[tex](4a^3+3a^2-2a+1)\times (-2a)=-8a^4-6a^3+4a^2-2a[/tex]
Hence, [tex]A=4a^2[/tex]
3. Multiply [tex]4a^3+3a^2-2a+1[/tex] by [tex]a^2:[/tex]
[tex](4a^3+3a^2-2a+1)\times a^2=4a^5+3a^4-2a^3+a^2[/tex]
Now, add all results:
[tex]\begin{array}{ccccccccccc}&&&&12a^3&+&9a^2&-&6a&+&3\\ \\&&-8a^4&-&6a^3&+&4a^2&-&2a&&\\ \\4a^5&+&3a^4&-&2a^3&+&a^2&&&&\\ \\ \\4a^5&-&5a^4&+&4a^3&+&14a^2&-&8a&+&3\end{array}[/tex]
Hence, [tex]B=4a^3[/tex]
