Question

Which shows a difference of squares? 10 y squared minus 4 x squared 16 y squared minus x squared 8 x squared minus 40 x + 25 64 x squared minus 48 x + 9

Answer 1

Answer:

B on edge

Step-by-step explanation:

just took

Answer 2

Answer:

16y² - x² shows a correct difference of squares.

Step-by-step explanation:

Following are the given options from which we have to chose which represents the difference of squares.

A) 10y² - 4x²

B) 16y² - x²

C) 8x² - 40x+25

D) 64x² - 48x+9

Difference of square is given by:

a² - b² = (a + b) (a - b)

If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.

As in option A) 10y² - 4x²

10y²  is not a complete square of any number. Hence, option A) is incorrect.

As in option C) 8x² - 40x+25

Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.

As in option D) 64x² - 48x+9

The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.

Lets take the expression 16y² - x²  of option B) and solve it.

First simplify the terms separately to associate them as perfect squares as shown below:

       ⇒  16y² = (4y)²        Equation (1)

       ⇒   x² = (1x)²           Equation (2)

Now, take the difference of Equation (1) and Equation (2).

        ⇒  16y² - x²

          ⇒ (4y)² - (1x)²       Equation (3)

So,

Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).

Which is  

               (4y - x) (4y + x) = 16y² - x²

                                         = (4y)² - (1x)²

So, option B) i.e. 16y² - x² shows a correct difference of squares.

Keywords: difference of square

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