Question

Which shows a difference of squares?

10y2 – 4x2
16y2 – x2
8x2 – 40x + 25
64x2 – 48x + 9

Answer 1

difference of two squares will be 

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

so the second choice 

Answer 2

Answer with explanation:

$1.\rightarrow 10y^2-x^2\\\\=(\sqrt{10}y)^2 -x^2$

Number 10, is not Square of any Integer.

So, we can't say  with surety that this expression is difference of squares.

$2. \rightarrow 16y^2-x^2\\\\= (4 y)^2 -x^2\\\\= (4 y-x)(4y+x)$

The Binomial expression has two terms , which are perfect Squares.So, it is difference of squares.

$3.\rightarrow 8x^2 - 40 x + 25\\\\=8 \times (x^2-5 x+3)+1\\\\=8 \times [(x-\frac{5}{2})^2-\frac{25}{4}+3]+1\\\\=8 \times [(x-\frac{5}{2})^2-\frac{13}{4}]+1\\\\=8 \times [(x-\frac{5}{2})^2]-\frac{13}{4}\times 8+1\\\\=8 \times [(x-\frac{5}{2})^2]-25\\\\=[2\sqrt{2}(x-\frac{5}{2})]^2-(5)^2$

Number , 8 is not perfect Square.So, we can't say with surety , it is not difference of squares.

$4\rightarrow 64x^2 - 48 x + 9\\\\=64\times(x^2-\frac{48x}{64}+\frac{9}{64})\\\\=64\times(x^2-\frac{3x}{4}+\frac{9}{64})\\\\=64 \times [(x-\frac{3}{8})^2-(\frac{3}{8})^2+\frac{9}{64}]\\\\=64 \times (x-\frac{3}{8})^2$

This expression is perfect Square number,not Difference of Squares.

⇒⇒Most Appropriate expression which is difference of squares

Option B

  $16y^2-x^2$