Chapter 8, Problem 19MCQ

To determine

To find the product of given two polynomials.

Answer to Problem 19MCQ

  $3x^3{y}^6-x^3{y}^4+2x^2{y}^6$

Explanation of Solution

Given:

  $x^2{y}^4\left(3x{y}^2-x+2y^2\right)$

Formula used:

Distributive Law:

  $x\left(y\pm z\right)=x\cdot y\pm x\cdot z$

Calculation:

Consider the given polynomials,

  $\Rightarrow x^2{y}^4\left(3x{y}^2-x+2y^2\right)$

  $\Rightarrow x^2{y}^4\cdot 3x{y}^2-x^2{y}^4\cdot x+x^2{y}^4\cdot 2y^2$  [ $\because$$x\left(y\pm z\right)=x\cdot y\pm x\cdot z$ ]

  $\Rightarrow 3x^3{y}^6-x^3{y}^4+2x^2{y}^6$

Conclusion:

Therefore, product of the given polynomials is $3x^3{y}^6-x^3{y}^4+2x^2{y}^6$ .