Question

go
find the product of each pair of conjugates.

1. ((x - 7)(x + 7))
2. ((2x + 9)(2x - 9))
3. ((5x + 3)(5x - 3))
4. ((a - b)(a + b))

pg. 58
access the full curriculum, supporting tools, and educator communities at openup.org.

Explanation:

Problem 17: \((x - 7)(x + 7)\)

Step1: Identify the formula

We use the difference of squares formula: \((a - b)(a + b)=a^{2}-b^{2}\). Here, \(a = x\) and \(b = 7\).

Step2: Apply the formula

Substitute \(a=x\) and \(b = 7\) into the formula: \(x^{2}-7^{2}\)

Step3: Simplify

Calculate \(7^{2}=49\), so the result is \(x^{2}-49\)

Step1: Identify the formula

Use the difference of squares formula: \((a - b)(a + b)=a^{2}-b^{2}\). Here, \(a = 2x\) and \(b = 9\).

Step2: Apply the formula

Substitute \(a = 2x\) and \(b=9\) into the formula: \((2x)^{2}-9^{2}\)

Step3: Simplify

Calculate \((2x)^{2}=4x^{2}\) and \(9^{2} = 81\), so the result is \(4x^{2}-81\)

Step1: Identify the formula

Use the difference of squares formula: \((a - b)(a + b)=a^{2}-b^{2}\). Here, \(a = 5x\) and \(b = 3\).

Step2: Apply the formula

Substitute \(a = 5x\) and \(b = 3\) into the formula: \((5x)^{2}-3^{2}\)

Step3: Simplify

Calculate \((5x)^{2}=25x^{2}\) and \(3^{2}=9\), so the result is \(25x^{2}-9\)

Answer:

\(x^{2}-49\)

Problem 18: \((2x + 9)(2x - 9)\)