QuestionFind and correct the error in Jeffrey's simplification of the expression: $c-2 x$ to $-7.5 x^{8} y^{13}$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $c-x$ . Jeffrey's work is as follows $\begin{array}{r} 3.32^{4}(3.5 \times y) \\ \left(- x^{} y^{3}\right)^{4}\left(3.5 x^{0} y\right) \\ \left(- x^{8} y^{12}\right)(3.5 y) \\ (- \cdot3.5)\left(x^{8}\right)\left(y^{12} \cdot y\right) \\ -7.5 x^{8} y^{13} \end{array}$

STEP 2

First, let's identify the error in Jeffrey's work. The error seems to be in the multiplication of $-2$ and $.5$ which gives $-7$ and not $-7.5$ .

STEP 3

Let's correct the error. The correct multiplication of $-2$ and $3.5$ is $-7$ .
$(-2 \cdot3.5)\left(x^{8}\right)\left(y^{12} \cdot y\right) = -7x^{8}y^{13}$

STEP 4

Now, let's check the rest of Jeffrey's work. The expression $\left(-2 x^{2} y^{3}\right)^{4}\left(3. x^{0} y\right)$ simplifies to $\left(-2 x^{8} y^{12}\right)(3. y)$ , which is correct.

STEP 5

The expression $\left(-2 x^{8} y^{12}\right)(3.5 y)$ simplifies to $-7x^{8}y^{13}$ , which is also correct.
So, the corrected version of Jeffrey's work is $\begin{array}{r} 3.32^{4}(3.5 \times y) \\ \left(-2 x^{2} y^{3}\right)^{4}\left(3.5 x^{0} y\right) \\ \left(-2 x^{8} y^{12}\right)(3.5 y) \\ (-2 \cdot3.5)\left(x^{8}\right)\left(y^{12} \cdot y\right) \\ -7 x^{8} y^{13} \end{array}$

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