Question

question 9 (multiple choice worth 1 points) (06.04 mc) find the product of (x − 5)². options: x² + 10x + 25, x² − 10x + 25, x² − 25, x² + 25. question 10 (multiple choice worth 1 points) (06.04 mc) write a simplified polynomial expression in standard form to represent the area of the rectangle below. rectangle with length 2x - 4 and width x + 5 options: 2x² + 6x − 20, 2x² − 4x − 20, 2x² + 6x + 20, 2x² + 10x + 20.

Explanation:

Question 9

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = x\) and \(b = 5\).

Step2: Apply the formula

Substitute \(a = x\) and \(b = 5\) into the formula:
\((x - 5)^2 = x^2 - 2\times x\times5 + 5^2\)

Step3: Simplify the expression

Calculate each term: \(x^2 - 10x + 25\)

Step1: Recall the formula for the area of a rectangle

The area of a rectangle is length \(\times\) width. Here, length is \(2x - 4\) and width is \(x + 5\).

Step2: Multiply the two binomials

Use the distributive property (FOIL method):
\((2x - 4)(x + 5)=2x\times x + 2x\times5 - 4\times x - 4\times5\)

Step3: Simplify each term

\(2x^2 + 10x - 4x - 20\)

Step4: Combine like terms

\(2x^2 + (10x - 4x) - 20 = 2x^2 + 6x - 20\)

Answer:

\(x^2 - 10x + 25\) (the second option)

Question 10