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\\\\=(√(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 * (x^2-5 x+3)+1\\\\=8 * [(x-(5)/(2))^2-(25)/(4)+3]+1\\\\=8 * [(x-(5)/(2))^2-(13)/(4)]+1\\\\=8 * [(x-(5)/(2))^2]-(13)/(4)* 8+1\\\\=8 * [(x-(5)/(2))^2]-25\\\\=[2√(2)(x-(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*(x^2-(48x)/(64)+(9)/(64))\\\\=64*(x^2-(3x)/(4)+(9)/(64))\\\\=64 * [(x-(3)/(8))^2-((3)/(8))^2+(9)/(64)]\\\\=64 * (x-(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`