Chapter 8.4, Problem 17MCQ

To determine

To find the product of given two polynomials.

Answer to Problem 17MCQ

  $-6x^{3}y-4x^2{y}^2+8x{y}^3$

Explanation of Solution

Given:

  $-2xy\left(3x^2+2xy-4y^2\right)$

Formula used:

Distributive Law:

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

Calculation:

Consider the given polynomials,

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

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

  $\Rightarrow -6x^{3}y-4x^2{y}^2+8x{y}^3$

Conclusion:

Therefore, product of the given polynomials is $-6x^{3}y-4x^2{y}^2+8x{y}^3$ .