Question

Multiply the following:

$25x{y}^2,8x^3+2x{y}^2+9x^{2}y+27y^3$

Answer 1

Finding the multiplication of algebraic expression

Multiplying by the horizontal method

$$\begin{gathered} 25x{y}^2(8x^3+2x{y}^2+9x^{2}y+27y^3)=\left(25x{y}^2\right)\times \left(8x^3\right)+\left(25x{y}^2\right)\times \left(2x{y}^2\right)+\left(25x{y}^2\right)\times \left(9x^{2}y\right)+\left(25x{y}^2\right)\times \left(27y^3\right) \\ =\left(25\times 8\right)\left(x{y}^2\times x^3\right)+\left(25\times 2\right)\left(x{y}^2\times x{y}^2\right)+\left(25\times 9\right)\left(x{y}^2\times x^{2}y\right)+\left(25\times 27\right)\left(x{y}^2\times y^3\right) \\ =200x^4{y}^2+50x^2{y}^4+225x^3{y}^3+675x{y}^5 \end{gathered}$$

Hence, the product of algebraic expression is $200x^4{y}^2+50x^2{y}^4+225x^3{y}^3+675x{y}^5$.