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Jlenok [28]
3 years ago
8

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
Mathematics
2 answers:
vodka [1.7K]3 years ago
8 0

Answer:

B on edge

Step-by-step explanation:

just took

evablogger [386]3 years ago
3 0

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

Learn more about completing the square from brainly.com/question/12829957

#learnwithBrainly

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