Suppose that the functions $r$ and $s$ are defined for all real numbers $x$ as follows.
$\begin{array}{l} r (x) = x^{3} \\ s (x) = 3 x^{2} \end{array}$
Write the expressions for $(s + r) (x)$ and $(s - r) (x)$ and evaluate $(s \cdot r) (- 2)$ .

Answer

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Answer

Thus, the expressions for $(s + r) (x)$ and $(s - r) (x)$ are $x^{3} + 3 x^{2}$ and $- x^{3} + 3 x^{2}$ respectively. The value of $(s \cdot r) (- 2)$ is $- 96$ .

Steps

Step 1 ：Let the functions $r$ and $s$ be defined as $r (x) = x^{3}$ and $s (x) = 3 x^{2}$ for all real numbers $x$ .

Step 2 ：To find the expression for $(s + r) (x)$ , we add the expressions for $s (x)$ and $r (x)$ together to get $x^{3} + 3 x^{2}$ .

Step 3 ：To find the expression for $(s - r) (x)$ , we subtract the expression for $r (x)$ from the expression for $s (x)$ to get $- x^{3} + 3 x^{2}$ .

Step 4 ：To evaluate $(s \cdot r) (- 2)$ , we multiply the expressions for $s (- 2)$ and $r (- 2)$ together to get $- 96$ .

Step 5 ：Thus, the expressions for $(s + r) (x)$ and $(s - r) (x)$ are $x^{3} + 3 x^{2}$ and $- x^{3} + 3 x^{2}$ respectively. The value of $(s \cdot r) (- 2)$ is $- 96$ .

Suppose that the functions r and s are defined for all real numbers x as follows.r(x)=x3s(x)=3x2Write the expressions for (s+r)(x) and (s−r)(x) and evaluate (s⋅r)(−2).

Answer

Popular Problems

Suppose that the functions $r$ and $s$ are defined for all real numbers $x$ as follows.
$\begin{array}{l} r (x) = x^{3} \\ s (x) = 3 x^{2} \end{array}$
Write the expressions for $(s + r) (x)$ and $(s - r) (x)$ and evaluate $(s \cdot r) (- 2)$ .