Question

which shows a difference of squares?
10y² - 4x²
16y² - x²
8x² - 40x + 25
64x² - 48x + 9

Explanation:

Step1: Recall difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\), where both terms are perfect squares and separated by a subtraction sign.

Step2: Analyze each option

• Option 1: \(10y^{2}-4x^{2}\)

The coefficient of \(y^{2}\) is \(10\), which is not a perfect square. So this is not a difference of squares.

• Option 2: \(16y^{2}-x^{2}\)

We can rewrite \(16y^{2}\) as \((4y)^{2}\) and \(x^{2}\) as \((x)^{2}\). So it is in the form \(a^{2}-b^{2}\) where \(a = 4y\) and \(b=x\).

• Option 3: \(8x^{2}-40x + 25\)

This is a quadratic trinomial (has three terms) and is not a difference of squares (needs two terms with subtraction).

• Option 4: \(64x^{2}-48x + 9\)

This is also a quadratic trinomial (three terms) and not a difference of squares.

Answer:

\(16y^{2}-x^{2}\) (the second option)