Question

Which shows a difference of squares?

Answer 1

Answer:

The expression which shows the difference  of squares is $(16y)^{2} - (x)^{2}$ .

Step-by-step explanation:

Here, the given expressions are :

$1. (10y)^{2} - (4x)^{2}\\2.(16y)^{2} - (x)^{2}\\3. (8x)^{2} - (4x + 25)\\4. (64x)^{2} - (48x + 9)$

Now, DIFFERENCE of SQUARES is an expression where one perfect square term is subtracted from another perfect square term.

And each difference of square can be expanded using algebraic identity

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

Now, here only the terms in expression 2 are perfect squares, as

$(16y)^{2} = (4y)^{2} =(-4y)^{2} , (x)^{2} = (x)^{2} =(-x)^{2}$

Hence, the expression which shows the difference  of squares is $(16y)^{2} - (x)^{2}$ .

Also, here$(16y)^{2} - (x)^{2} = (4y-x)(4y+x)$

Answer 2

Answer:

Option A and B.

Step-by-step explanation:

We need to find the expression which shows a difference of squares.

Difference of squares:

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

The given expression can be written as

$10y^2-4x^2=(\sqrt{10}y)^2-(2x)^2$

The expression $10y^2-4x^2$ represents shows a difference of squares.

Second expression is

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

The expression $16y^2-x^2$ represents shows a difference of squares.

Third expression is

$8x^2-40x+25$

It can not be written as difference of squares.

Fourth expression is

$64x^2-48 x + 9$

$(8x)^2-2(8)(3) x + 3^2$

$(8x-3)^2$

It can not be written as difference of squares.

Therefore, the correct options are A and B.