Chapter 8, Problem 47SGR

To determine

To factorize the given expression.

Answer to Problem 47SGR

  $3f^4{g}^2(6g^3-f^2+3g)$

Explanation of Solution

Given:

Expression: $18f^4{g}^5-3f^6{g}^2+9f^4{g}^3$

Concept used:

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

Calculation:

Consider the expression $18f^4{g}^5-3f^6{g}^2+9f^4{g}^3$ ,

Finding the common term and simplifying using distributive property,

  $\begin{array}{l}\Rightarrow 18f^4{g}^5-3f^6{g}^2+9f^4{g}^3\\ \Rightarrow 3f^4{g}^2(6g^3-f^2+3g)\end{array}$

Conclusion:

Therefore, the factors of the given expression are $3f^4{g}^2(6g^3-f^2+3g).$