Question

Which shows a difference of squares?


10y^2−4x^2



16y^4−x^2



8x^2−40x+25



64x^2−48x+9

Answer 1

A difference of squares must be a binomial, so we want two terms. This rules out the third and fourth options.

If we look at the first two, we must check that both terms are perfect squares.

Look at the first one: $4x^2$ is a perfect square (it's $(2x)^2$), but $10y^2$ is not a perfect square, because 10 is not a perfect square.

On the other hand, if we look at the second option, $16y^4$ is the square of $4y^2$, and $x^2$ is clearly the square of $x$. So, this is the difference of two squares.