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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