Answer:
16y² - x² shows a correct difference of squares.
Step-by-step explanation:
<em>Following are the given options from which we have to chose which represents the difference of squares. </em>
<em>A) 10y² - 4x²</em>
<em>B) 16y² - x²</em>
<em>C) 8x² - 40x+25</em>
<em>D) 64x² - 48x+9</em>
<em>Difference of square is given by: </em>
<em>a² - b² = (a + b) (a - b)</em>
<em>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.</em>
<em>As in option A) 10y² - 4x²</em>
10y² is not a complete square of any number. Hence, option A) is incorrect.
<em>As in option C) 8x² - 40x+25</em>
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.
<em>Lets take the expression 16y² - x² of option B) and solve it.</em>
First simplify the terms separately to associate them as perfect squares as shown below:
⇒ 16y² = (4y)² <em>Equation (1)</em>
⇒ x² = (1x)² <em>Equation (2)</em>
Now, take the difference of <em>Equation (1) and Equation (2).</em>
<em> </em> ⇒<em> </em>16y² - x²
⇒ (4y)² - (1x)² <em>Equation (3)</em>
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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