Q8. - Algebra 1

Question

Choose a term from the Key Vocabulary list above that best describes the given expression.

$\left(x+2\right)\left(x-5\right)=x^2-3x-10$

Step-by-Step Solution

Answer

The given expression can be best described as the FOIL method.

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define FOIL method.

FOIL method is used to multiply two binomials.

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

Step 3. Write the best description for the expression, x + 2 x − 5 = x 2 − 3 x − 10 .

Observe the expression, $\left(x+2\right)\left(x-5\right)=x^2-3x-10$.

$$\begin{gathered} \left(x+2\right)\left(x-5\right)=\left(x\right)\left(x\right)+\left(x\right)\left(-5\right)+\left(2\right)\left(x\right)+\left(2\right)\left(-5\right) \\ =x^2-5x+2x-10 \\ =x^2-3x-10 \end{gathered}$$

The expression, $\left(x+2\right)\left(x-5\right)=x^2-3x-10$ involves the product of two binomials $\left(x+2\right)$ and $\left(x-5\right)$ by using the FOIL method.

 

Therefore the given expression can be best described as the FOIL method.