12 perform the indicated operations and simplify 4 a3 2 16

12. perform the indicated operations and simplify.

( 4 a^3 2 )( 16 a^4 + 12 a^2 + 5 )

Solution

(4a³ 2)(16a⁴ + 12 a² + 5)

= 4a³(16a⁴ + 12 a² + 5) -2(16a⁴ + 12 a² + 5)

= 64a³⁺⁴ + 48a³⁺² + 20a³ -32a⁴ -24a² -10       since a^m * aⁿ = a^m+n

= 64a⁷ + 48a⁵ -32a⁴ + 20a³ - 24a² -10

Hence (4a³ 2)(16a⁴ + 12 a² + 5) = 64a⁷ + 48a⁵ -32a⁴ + 20a³ - 24a² -10