Question

What is the resultant polynomial obtained when the given polynomials $\left(a^3\right)$ and $(51c{b}^2+14abc)$ are multiplied?

• A. $51c{b}^2{a}^3+14a+a^{4}bc$
• B. $51abc+14a^{3}bc$
• C. $51cb{a}^2+14a^{3}bc$
• D. $51a^3{b}^{2}c+14a^{4}bc$

Answer 1

The correct option is D $51a^3{b}^{2}c+14a^{4}bc$

In the given question, a monomial is multiplied with a binomial.
$a^3(51c{b}^2+14abc)$
$=51c{b}^2\left(a^3\right)+14abc\left(a^3\right)$
$=51a^3{b}^{2}c+14a^{4}bc$