Question

for questions 6 - 8, find the products for each special case.

1. ((2x + 1)^2) 7. ((2x + 6)(2x - 6))

9.3.2 checkup: practice problems
copyright © 2023 apex learning inc. use of this material is subject to apex learnings terms of use. any unauthorized copying, reuse, or redistribution is prohibited.

1. ((x - 8)^2)

Explanation:

Problem 6: \((2x + 1)^2\)

Step 1: Recall the square of a binomial formula

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 2x\) and \(b = 1\).

Step 2: Apply the formula

First, calculate \(a^2=(2x)^2 = 4x^2\).
Then, calculate \(2ab = 2\times(2x)\times1=4x\).
Next, calculate \(b^2 = 1^2 = 1\).

Step 3: Combine the terms

Add the three terms together: \(4x^2 + 4x + 1\).

Step 1: Recall the difference of squares formula

The formula for \((a + b)(a - b)\) is \(a^2 - b^2\). Here, \(a = 2x\) and \(b = 6\).

Step 2: Apply the formula

Calculate \(a^2=(2x)^2 = 4x^2\) and \(b^2 = 6^2 = 36\).
Then, subtract: \(4x^2 - 36\).

Step 1: Recall the square of a binomial formula

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = x\) and \(b = 8\).

Step 2: Apply the formula

First, calculate \(a^2 = x^2\).
Then, calculate \(2ab = 2\times x\times8 = 16x\).
Next, calculate \(b^2 = 8^2 = 64\).

Step 3: Combine the terms

Subtract and add the terms: \(x^2 - 16x + 64\).

Answer:

\(4x^2 + 4x + 1\)

Problem 7: \((2x + 6)(2x - 6)\)