Multiply Binomials: Solve (x-9)(x+√9) Step by Step

In order to solve this problem, we'll follow these steps:

• Step 1: Simplify the expression inside the binomials

• Step 2: Apply the FOIL method to expand the product of binomials

• Step 3: Combine like terms to find the final expression

Let's proceed to work through each step:

Step 1: Simplify the expression inside the binomials

The original expression is $(x-9)(x+\sqrt{9})$. First, we simplify $\sqrt{9}$, which equals $3$. Thus, the expression becomes $(x-9)(x+3)$.

Step 2: Apply the FOIL method to expand the product

Using the FOIL method, which stands for First, Outside, Inside, and Last, we expand as follows:

• First: Multiply the first terms: $x \cdot x = x^2$

• Outside: Multiply the outside terms: $x \cdot 3 = 3x$

• Inside: Multiply the inside terms: $-9 \cdot x = -9x$

• Last: Multiply the last terms: $-9 \cdot 3 = -27$

Step 3: Combine like terms

Now, combine the results: $x^2 + 3x - 9x - 27$.

Combine the like terms $3x$ and $-9x$, resulting in $-6x$.

The final expanded form of the expression is $x^2 - 6x - 27$.

Comparing our result with the given choices, the correct choice is:

$x^2-6x-27$

Therefore, the solution to the problem is $x^2 - 6x - 27$.