Chapter 4.6, Problem 14OE

To determine

To complete: the blank with appropriate expression

Answer to Problem 14OE

Expanding the given expression we get $\boxed{\left(\underset{\_}{1\text{}}\right)x^2+\left(\underset{\_}{2}\right)x-\left(\underset{\_}{15\text{}}\right)}$

Explanation of Solution

Given information: $\left(x-3\right)\left(x+5\right)=\left(x-3\right)x+\left(x-3\right)5=\left(\underset{\_}{?}\right)x^2+\left(\underset{\_}{?}\right)x-\left(\underset{\_}{?}\right)$

Concept Involved:

Distribute the x and 5 by multiply it with each term inside the parenthesis. Then combine like terms to get the final answer

Calculation:

Distribute the x and 5 by multiply it with each term inside the parenthesis

  $x^2-3x+5x-15$

Combine like terms

  $x^2+2x-15$

Conclusion:

The complete equation is $\left(x-3\right)\left(x+5\right)=\left(x-3\right)x+\left(x-3\right)5=\boxed{\left(\underset{\_}{1\text{}}\right)x^2+\left(\underset{\_}{2}\right)x-\left(\underset{\_}{15\text{}}\right)}$