Chapter 4, Problem 12CR

To determine

To simplify the expression $\left(c-6\right)\left(c^2+2c+3\right)$ .

Answer to Problem 12CR

  $c.c^3-4c^2-9c-18$

Explanation of Solution

Given information:

The expression, $\left(c-6\right)\left(c^2+2c+3\right)$

Concept used:

• The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$
• Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression, use the distributive property of binomials (FOIL) to multiply the binomials and then simplify further by using the exponent property as shown below

  $\begin{array}{c}\left(c-6\right)\left(c^2+2c+3\right)=c\cdot \left(c^2+2c+3\right)-6\cdot \left(c^2+2c+3\right)\\ =c\cdot c^2+c\cdot 2c+c\cdot 3-6\cdot c^2-6\cdot 2c-6\cdot 3\\ =c^3+2c^2+3c-6c^2-12c-18\\ =c^3-4c^2-9c-18\end{array}$

Thus, the given expression simplifies to $c^3-4c^2-9c-18$ .