Question

which expression is a difference of squares with a factor of 2x + 5?
○ 4x² + 10
○ 4x² − 10
○ 4x² + 25
○ 4x² − 25

Explanation:

Step1: Recall difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Analyze the given factor \(2x + 5\)

If one factor is \(2x+5\), then from the difference of squares formula, the other factor should be \(2x - 5\) (since \((a + b)(a - b)\) where \(a = 2x\) and \(b=5\)).

Step3: Multiply the two factors \((2x + 5)(2x - 5)\)

Using the formula \((a + b)(a - b)=a^2-b^2\), here \(a = 2x\) and \(b = 5\). So \((2x)^2-5^2=4x^2 - 25\).

Step4: Check other options

• For \(4x^2+10\): It is not a difference of squares (it has a plus sign and 10 is not a perfect square).
• For \(4x^2 - 10\): 10 is not a perfect square, so it is not a difference of squares.
• For \(4x^2+25\): It is a sum of squares, not a difference of squares.

Answer:

\(4x^2 - 25\) (corresponding to the last option)