Chapter SR11, Problem 27P

Solution

To simplify the expression $\left(-4z+3\right)\left(6z-1\right)$ .

  $-24z^2+22z-3$

Given:

The expression, $\left(-4z+3\right)\left(6z-1\right)$

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 $\left(-4z+3\right)\left(6z-1\right)$ , use the FOIL method to multiply the binomials and then simplify further by combining the like terms as shown below

  $\begin{array}{c}\left(-4z+3\right)\left(6z-1\right)=\left(-4z\right)\cdot 6z+\left(-4z\right)\cdot \left(-1\right)+3\cdot 6z+3\cdot \left(-1\right)\\ =-24z^2+4z+18z-3\\ =-24z^2+22z-3\end{array}$

Thus, the given expression simplifies to $-24z^2+22z-3$ .