Determine whether the polynomial is a difference of squares and if it is, factor it.

Mathematics

2 answers:

Paha777 [63]3 years ago

8 0

The answer is C
y² - 25
= y² - 5²
= (y + 5)(y - 5) which is a difference of two squares

LenaWriter [7]3 years ago

6 0

<h2>Answer:</h2>

Option: C is the correct answer.

C. Is a difference of squares: (y + 5)(y − 5).

<h2>Step-by-step explanation:</h2>

We are given a polynomial expression in terms of the variable y as follows:

$y^2-25$

Now this expression could also be written as:

$y^2-25=y^2-5^2$

This means that the expression is a difference of squares.

Also, we know that:

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

Here,

$a=y\ and\ b=5$

Hence,

$y^2-25=(y+5)(y-5)$

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1) The x-axis represents the energy ( $E$ ), in joules. The y-axis represents the amplitude ( $x$ ), in milimeters.

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3) The amplitude is directly proportional to the root square of the energy.

<h3>How to analyze a graph relationship between two variables</h3>

In this question we have a relationship between two variables, in which we must apply principles of <em>functional</em> analysis to respond three questions presented in the statement.

Now we proceed to answer the three questions below:

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<em>How would you describe the rate of change of the line?</em> R/ The curve depicts an <em>monotonous decrecent</em> rate of change, that is, the slope converges to zero when the energy tends to infinite.
<em>What does this tell you about the relationship between amplitude and energy?</em> R/ The curve show a strong similarity with a function of the form $x = A\cdot \sqrt{E}$ . Hence, the amplitude is directly proportional to the root square of the energy.