Chapter 11, Problem 1P

To determine

(a)

The interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$; 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,

$S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$

$S_2={\left(2x-3\right)}^2+4x$

Multiply the above expressions.

$\begin{array}{c}{S}_1\cdot S_2=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)\cdot \left[{\left(2x-3\right)}^2+4x\right]\\ =-(4x+{(}^2)(x^2(-4x^2+8x+3)-24x+27)\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. Determine the simplest form of $S_1\cdot S_2$ using symbolic operation.

MATLAB Code:

syms x

S1 = x.^2.*(4.*x.^2-8.*x-3)+3.*(8.*x-9)

S2 = (2.*x-3).^2+4.*x

a = simplify(S1.*S2)

Save the MATLAB script with the name, Chapter11_56830_11_1Pa.m in the current folder. Execute the script by typing the script name at the command window to get the code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. 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: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$; 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,

$S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$

$S_2={\left(2x-3\right)}^2+4x$

Divide the above expressions.

$\begin{array}{c}\frac{S_1}{S_2}=\frac{x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)}{\left[{\left(2x-3\right)}^2+4x\right]}\\ =x^2-3\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. Determine the simplest form of $\frac{S_1}{S_2}$ using symbolic operation.

MATLAB Code:

syms x

S1 = x.^2.*(4.*x.^2-8.*x-3)+3.*(8.*x-9)

S2 = (2.*x-3).^2+4.*x

b = simplify(S1./S2)

Save the MATLAB script with the name, Chapter11_56830_11_1Pb.m in the current folder. Execute the script by typing the script name at the command window to get the code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. 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: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$; 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,

$S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$

$S_2={\left(2x-3\right)}^2+4x$

Subtract the above expressions.

$\begin{array}{c}{S}_1-S_2=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)-\left[{\left(2x-3\right)}^2+4x\right]\\ =4x^4-8x^3-7x^2+32x-36\end{array}$

Write the MATLAB code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. Determine the simplest form of $S_1-S_2$ using symbolic operation.

MATLAB Code:

syms x

S1 = x.^2.*(4.*x.^2-8.*x-3)+3.*(8.*x-9)

S2 = (2.*x-3).^2+4.*x

b = simplify(S1-S2)

Save the MATLAB script with the name, Chapter11_56830_11_1Pc.m in the current folder. Execute the script by typing the script name at the command window to get the code to determine the interpretation of $x$ and $y$ as symbolic variables and create the two symbolic expressions: $S_1=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)$ and $S_2={\left(2x-3\right)}^2+4x$. 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 $x=7$ using $\text{subs}$ command.

Answer to Problem 1P

Solution:

The program is stated as follows.

Explanation of Solution

The given expressions are,

Subtract the above expressions.

$\begin{array}{c}{S}_1-S_2=x^2\left(4x^2-8x-3\right)+3\left(8x-9\right)-\left[{\left(2x-3\right)}^2+4x\right]\\ =4x^4-8x^3-7x^2+32x-36\end{array}$

Substitute $x=7$ in the above equation.

$\begin{array}{c}f\left(7\right)=4{\left(7\right)}^4-8{\left(7\right)}^3-7{\left(7\right)}^2+32\left(7\right)-36\\ =6707\end{array}$

Write the MATLAB code to determine the numerical value of the result from part (c) for $x=7$ using $\text{subs}$ command.

MATLAB Code:

syms x

S1 = x.^2.*(4.*x.^2-8.*x-3)+3.*(8.*x-9)

S2 = (2.*x-3).^2+4.*x

c = simplify(S1-S2);

d = subs(c,7)

Save the MATLAB script with the name, Chapter11_56830_11_1Pd.m in the current folder. Execute the script by typing the script name at the command window to get the code to determine the numerical value of the result from part (c) for $x=7$ using $\text{subs}$ command.

Result:

Conclusion:

Therefore, the required program is executed above.