Chapter 8, Problem 42SGR

To determine

To use distributive property to factor the given polynomial.

Answer to Problem 42SGR

  $(x-y)(2x-3z)$

Explanation of Solution

Given:

Polynomial: $2x^2-3xz-2xy+3yz$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the polynomial $2x^2-3xz-2xy+3yz$ ,

Grouping the similar terms,

  $\begin{array}{l}\Rightarrow 2x^2-3xz-2xy+3yz\\ \Rightarrow (2x^2-2xy)+(3yz-3xz)\end{array}$

Applying the distributive property,

Finding out the common terms in each term of the expression,

Here, $(2x-3z)$ is common term.

  $\begin{array}{l}\Rightarrow (2x^2-3xz)+(-2xy+3yz)\\ \Rightarrow x(2x-3z)-y(2x-3z)\\ \Rightarrow (x-y)(2x-3z)\end{array}$

Conclusion:

Therefore, the factors of the given polynomial are $(x-y)(2x-3z).$