Chapter 1.2, Problem 54PPE

a.

To determine

To evaluate the given expressions for $x=1$ and $y=0$

Answer to Problem 54PPE

  $1,1$

Explanation of Solution

Given:

The given expressions are ${(x+y)}^2$ and $x^2+y^2$

Calculation:

Substituting the values $x=1$ and $y=0$ in given expressions-

  $\begin{array}{l}{(x+y)}^2\\ ={(1+0)}^2\\ =1\end{array}$

  $\begin{array}{l}{x}^2+y^2\\ =1^2+0^2\\ =1\end{array}$

b.

To determine

To evaluate the given expressions for $x=1$ and $y=2$

Answer to Problem 54PPE

  $9,5$

Explanation of Solution

Given:

The given expressions are ${(x+y)}^2$ and $x^2+y^2$

Calculation:

Substituting the values $x=1$ and $y=2$ in given expressions-

  $\begin{array}{l}{(x+y)}^2\\ ={(1+2)}^2\\ =3^2=9\end{array}$

  $\begin{array}{l}{x}^2+y^2\\ =1^2+2^2\\ =1+4\\ =5\end{array}$

c.

To determine

To choose another pair for evaluating the expression.

Answer to Problem 54PPE

  $9,5$

Explanation of Solution

Given:

The given expressions are ${(x+y)}^2$ and $x^2+y^2$

Calculation:

Substituting the values $x=2$ and $y=3$ in given expressions-

  $\begin{array}{l}{(x+y)}^2\\ ={(2+3)}^2\\ =5^2=25\end{array}$

  $\begin{array}{l}{x}^2+y^2\\ =2^2+3^2\\ =4+9\\ =13\end{array}$

d.

To determine

To find out whether the claim made by student is correct or not.

Answer to Problem 54PPE

No.

Explanation of Solution

Given:

The student claimed that ${(x+y)}^2$ and $x^2+y^2$ are the same expression.

Calculation:

The claim is totally incorrect as the result obtained is different not the same which can be seen from part (b) and part (c).