Chapter 11, Problem 1P

To determine

(a)

The interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$; the simplest form of $S_1\cdot S_2$ using symbolic operation.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given expressions are,

$S_1=x^2\left(x-6\right)+4\left(3x-2\right)$

$S_2={\left(x+2\right)}^2-8x$

Multiply the above expressions.

$\begin{array}{c}{S}_1\cdot S_2=\left[x^2\left(x-6\right)+4\left(3x-2\right)\right]\cdot \left[{\left(x+2\right)}^2-8x\right]\\ =12x+x^2\left(x-6\right)-8\cdot \left[{\left(x+2\right)}^2-8x\right]\\ ={(}^x\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $S_1\cdot S_2$ using symbolic operation.

MATLAB Code:

syms x

S1 = x^2*(x-6)+4*(3*x-2)

%Define the expression S1.

S2 = (x+2)^2-8*x

%Define the expression S2.

result = simplify(S1.*S2)

%Multiply the given expression

Save the MATLAB script with name, Chapter11_29864_11_1Pa.m in the current folder. Execute the script by typing the script name at the command window to get the code that determinestheinterpretation of $x$ and $y$ as symbolic variables and creates the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $S_1\cdot S_2$ using symbolic operation.

Result:

Conclusion:

Therefore, the required program is executed above.

To determine

(b)

The interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$; the simplest form of $\frac{S_1}{S_2}$ using symbolic operation.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given expressions are,

$S_1=x^2\left(x-6\right)+4\left(3x-2\right)$

$S_2={\left(x+2\right)}^2-8x$

Divide the above expressions.

$\begin{array}{c}\frac{S_1}{S_2}=\frac{x^2\left(x-6\right)+4\left(3x-2\right)}{\left[{\left(x+2\right)}^2-8x\right]}\\ =\frac{12x+x^2\left(x-6\right)-8}{\left[{\left(x+2\right)}^2-8x\right]}\\ =x-2\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $\frac{S_1}{S_2}$ using symbolic operation.

MATLAB Code:

syms x

S1 = x^2*(x-6)+4*(3*x-2)

%Define the expression S1.

S2 = (x+2)^2-8*x

%Define the expression S2.

result = simplify(S1./S2)

%Divide the given expression

Save the MATLAB script with name, Chapter11_29864_11_1Pb.m in the current folder. Execute the script by typing the script name at the command window to get the code that determinestheinterpretation of $x$ and $y$ as symbolic variables and creates the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $\frac{S_1}{S_2}$ using symbolic operation.

Result:

Conclusion:

Therefore, the required program is executed above.

To determine

(c)

The interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$; the simplest form of $S_1+S_2$ using symbolic operation.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given expressions are,

$S_1=x^2\left(x-6\right)+4\left(3x-2\right)$

$S_2={\left(x+2\right)}^2-8x$

Add the above expressions.

$\begin{array}{c}{S}_1+S_2=\left[x^2\left(x-6\right)+4\left(3x-2\right)\right]+\\ =\left[12x+x^2\left(x-6\right)-8\right]+\left[{\left(x+2\right)}^2-8x\right]\\ =(x-1){(}^x\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $S_1+S_2$ using symbolic operation.

MATLAB Code:

syms x

S1 = x^2*(x-6)+4*(3*x-2)

%Define the expression S1.

S2 = (x+2)^2-8*x

%Define the expression S2.

result = simplify(S1+S2)

%Add the given expression

Save the MATLAB script with name, Chapter11_29864_11_1Pc.m in the current folder. Execute the script by typing the script name at the command window to get the code that determinestheinterpretation of $x$ and $y$ as symbolic variables and creates the two symbolic expressions: $S_1=x^2\left(x-6\right)+4\left(3x-2\right)$ and $S_2={\left(x+2\right)}^2-8x$. Determine the simplest form of $S_1+S_2$ using symbolic operation.

Result:

Conclusion:

Therefore, the required program is executed above.

To determine

(d)

The numerical value of the result from part (c) for $x=5$ using $\text{subs}$ command.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given expressions are,

$S_1=x^2\left(x-6\right)+4\left(3x-2\right)$

$S_2={\left(x+2\right)}^2-8x$

Add the above expressions.

$\begin{array}{c}{S}_1+S_2=\left[x^2\left(x-6\right)+4\left(3x-2\right)\right]+\\ =\left[12x+x^2\left(x-6\right)-8\right]+\left[{\left(x+2\right)}^2-8x\right]\\ =(x-1){(}^x\end{array}$

Substitute $x=5$ in the above equation.

$\begin{array}{c}f\left(5\right)=(5-1){(}^5\\ =36\end{array}$

Write the MATLAB code to determine the numerical value of the result from part (c) for $x=5$ using $\text{subs}$ command.

MATLAB Code:

syms x

S1 = x^2*(x-6)+4*(3*x-2);

%Define the expression S1.

S2 = (x+2)^2-8*x;

%Define the expression S2.

result = simplify(S1+S2);

%Add the given expression

result_at_5 = subs(result,5)

Save the MATLAB script with name, Chapter11_29864_11_1Pd.m in the current folder. Execute the script by typing the script name at the command window to get the code that determinesthenumerical value of the result from part (c) for $x=5$ using $\text{subs}$ command.

Result:

Conclusion:

Therefore, the required program is executed above.