Question

Multiply $\frac{1}{2}{a}^{2}b-\frac{2}{3}a{b}^2+5by6abc$

Answer 1

Multiplication of algebraic expression

Multiplying each term of the polynomial by the monomial.

$\begin{array}{rcl}\frac{1}{2}{a}^{2}b-\frac{2}{3}a{b}^2+5by6abc& =& 6abc\times (\frac{1}{2}{a}^{2}b-\frac{2}{3}a{b}^2+5)\\ & =& 6\times \frac{1}{2}abc\times a^{2}b-6\times \frac{2}{3}\times abc\times a{b}^2+6\times 5\times abc\\ & =& 3a^3{b}^{2}c-4a^2{b}^{3}c+30abc\end{array}$

Therefore, the product is $3a^3{b}^{2}c-4a^2{b}^{3}c+30abc$.