Question

which shows a difference of squares?

\\(10y^2 - 4x^2\\)
\\(16y^2 - x^2\\)
\\(8x^2 - 40x + 25\\)
\\(64x^2 - 48x + 9\\)

Explanation:

Define difference of squares

A difference of squares is an algebraic expression of the form:

$$ a^2 - b^2 = (a - b)(a + b) $$

Both terms must be perfect squares separated by a subtraction sign.

Analyze each option

• \(10y^2 - 4x^2\): The coefficient \(10\) is not a perfect square integer.
• \(16y^2 - x^2\): Both terms are perfect squares: \(16y^2 = (4y)^2\) and \(x^2 = (x)^2\), separated by subtraction.
• \(8x^2 - 40x + 25\): This is a trinomial, not a binomial difference of squares.
• \(64x^2 - 48x + 9\): This is a trinomial, not a binomial difference of squares.

Identify the correct choice

The expression \(16y^2 - x^2\) represents a difference of squares because:

$$ 16y^2 - x^2 = (4y)^2 - (x)^2 $$

Answer:

• (A) \(10y^2-4x^2\)
• (B) \(16y^2-x^2\) (Correct answer)
• (C) \(8x^2-40x+25\)
• (D) \(64x^2-48x+9\)