Activity An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms? Complete the steps below to solve this problem and others like it.
Part A
Three electrons are removed from each of 4 atoms. Write an expression to represent the net change on the charge for the group of atoms.

Part B
Simplify the expression obtained in part A and explain what the answer represents.

Part C
Here’s a similar problem. Write an expression for the net change in charge if two electrons are added to each of six atoms in a group. Also, write an expression that represents removing two protons each from a group of six atoms.

Part D
Simplify the two expressions in part C.

Part E
How are the two products in part D related?

Part F
Think about multiplying any two rational numbers. Based on this activity and your previous work, write a set of rules for finding the sign of the product based on the sign of the two numbers being multiplied.

Step-by-step explanation:

A: The charge of each electron is -1, so the charge of three electrons is -3. Removing something is denoted by a negative sign. The expression that represents the removal of three electrons from each of four atoms is (-3)(-4).

B: (-3)(-4) = (-1)(3)(-1)(4) = (-1)(-1)(3)(4) = 12

The net change in the charge for the group of atoms is 12 (or +12); that is, the charge of the atoms increases by 12.

C: Adding two electrons to each of six atoms results in a net change in charge of (-2)(6). Removing two protons from each of six atoms results in a net change in charge of (2)(-6).

D: (-2)(6) = (-1)(2)(6) = (-1)(12) = -12

(2)(-6) = (2)(6)(-1) = (12)(-1) = -12

E: The products are the same: -12.

F: If the signs of the numbers are the same, the product is positive. If the signs of the numbers are different, the product is negative.

A)

The charge of each electron is -1, so the charge of three electrons is -3. Removing something is denoted by a negative sign. The expression that represents the removal of three electrons from each of four atoms is (-3)(-4).

B)

(-3)(-4) = (-1)(3)(-1)(4) = (-1)(-1)(3)(4) = 12

The net change in the charge for the group of atoms is 12 (or +12); that is, the charge of the atoms increases by 12.

C)

Adding two electrons to each of six atoms results in a net change in charge of (-2)(6). Removing two protons from each of six atoms results in a net change in charge of (2)(-6).

D)

(-2)(6) = (-1)(2)(6) = (-1)(12) = -12

(2)(-6) = (2)(6)(-1) = (12)(-1) = -12

E)

The products are the same: -12.

F)

If the signs of the numbers are the same, the product is positive. If the signs of the numbers are different, the product is negative.

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step-by-step explanation:

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(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3