Chapter 4.6, Problem 13OE

To determine

To complete: the blank with appropriate expression

Answer to Problem 13OE

Expanding the given expression we get $\boxed{\left(\underset{\_}{1\text{}}\right)x^2+\left(\underset{\_}{5}\right)x+\left(\underset{\_}{6\text{}}\right)}$

Explanation of Solution

Given information: $\left(x+2\right)\left(x+3\right)=\left(x+2\right)x+\left(x+2\right)3=\left(\underset{\_}{?}\right)x^2+\left(\underset{\_}{?}\right)x+\left(\underset{\_}{?}\right)$

Concept Involved:

Distribute the x and 3 by multiply it with each term inside the parenthesis. Then combine like terms to get the final answer

Calculation:

Distribute the x and 3 by multiply it with each term inside the parenthesis

  $x^2+2x+3x+6$

Combine like terms

  $x^2+5x+6$

Conclusion:

The complete equation is $\left(x+2\right)\left(x+3\right)=\left(x+2\right)x+\left(x+2\right)3=\boxed{\left(\underset{\_}{1\text{}}\right)x^2+\left(\underset{\_}{5}\right)x+\left(\underset{\_}{6\text{}}\right)}$