Chapter 8.4, Problem 18MCQ

To determine

To find the product of given two polynomials.

Answer to Problem 18MCQ

  $12a^2{b}^2+5a{b}^3-a^2{b}^3$

Explanation of Solution

Given:

  $a{b}^2\left(12a+5b-ab\right)$

Formula used:

Distributive Law:

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

Calculation:

Consider the given polynomials,

  $\Rightarrow a{b}^2\left(12a+5b-ab\right)$

  $\Rightarrow a{b}^2\cdot 12a+a{b}^2\cdot 5b-a{b}^2\cdot ab$      [ $\because$$x\left(y\pm z\right)=x\cdot y\pm x\cdot z$ ]

  $\Rightarrow 12a^2{b}^2+5a{b}^3-a^2{b}^3$

Conclusion:

Therefore, product of the given polynomials is $12a^2{b}^2+5a{b}^3-a^2{b}^3$ .