Question

Emmeline is working on one side of a polynomial identity proof usedto form Pythagorean triples. Her work is shown below:(5x)2 + (5x2 - 5)2-Step 1: 25x2 + (5x2 – 5)2Step 2: 25x2 + 25x2 + 25Step 3: 50x2 + 25Step 4: 75x2What statement is true regarding Emmeline's work?(1) Emmeline's work is entirely correct.(2) There is a mistake in step 2, only.(3) There are mistakes in step 2 and step 4.(4) There is a mistake in step 4, only.

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

$\begin{gathered} Given\text{ the expression:} \\ (5x)^2\text{ + \lparen5x}^2\text{ - 5 \rparen}^2 \\ =\text{ 25 x}^2\text{ + 25x}^4\text{ - 50 x}^2\text{ + 25} \end{gathered}$

Hence, it is easy to see that

1)

$Emmeline^{\prime}s\text{ work is entirely incorrect \lparen OPTION A \rparen}$