Chapter SR11, Problem 1P

Solution

To simplify the expression $\left(a+5\right)\left(a+3\right)$ .

  $a^2+8a+15$

Given:

The expression, $\left(a+5\right)\left(a+3\right)$

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 $\left(a+5\right)\left(a+3\right)$ , use the FOIL method to multiply the binomials and then simplify further by combining the like terms as shown below

  $\begin{array}{c}\left(a+5\right)\left(a+3\right)=a\cdot a+a\cdot 3+5\cdot a+5\cdot 3\\ =a^2+3a+5a+15\\ =a^2+8a+15\end{array}$

Thus, the given expression simplifies to $a^2+8a+15$ .