Chapter SR11, Problem 18P

Solution

To simplify the expression $\left(3x-8\right)\left(x-6\right)$ .

  $3x^2-26x+48$

Given:

The expression, $\left(3x-8\right)\left(x-6\right)$

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$
• Distributing negative sign inside the parenthesis will change the sign of all terms inside the parenthesis.
• Product of powers property, $a^n\cdot a^m=a^{n+m}$
• FOIL to multiply binomials, $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

Calculation:

In order to simplify the given expression $\left(3x-8\right)\left(x-6\right)$ , use the FOIL method to multiply the binomials and then simplify further by combining the like terms as shown below

  $\begin{array}{c}\left(3x-8\right)\left(x-6\right)=3x\cdot x+3x\cdot \left(-6\right)+\left(-8\right)\cdot x+\left(-8\right)\cdot \left(-6\right)\\ =3x^2-18x-8x+48\\ =3x^2-26x+48\end{array}$

Thus, the given expression simplifies to $3x^2-26x+48$ .