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Physics: High School18 chapters | 212 lessons

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Lesson Transcript

Instructor:
*Damien Howard*

Damien has a master's degree in physics and has taught physics lab to college students.

There's quite a lot of algebra you need to know to do physics. Here we'll review some of the concepts needed for rearranging equations, working with polynomials, and working with exponents.

It's no secret that many students find physics to be one of the harder classes they take. Part of the reason for this is that not only is physics very math intensive, but it also won't teach you the math you need to take it. If you're taking an algebra or calculus-based physics course, it is assumed that you already know the math necessary for it.

While we can't possibly go over every algebra concept in this lesson that might pop up in a physics course, we can review some of the algebra concepts that come up the most often in physics.

One of the most common things you will be doing with algebra in a physics course is rearranging physics equations. You may be doing this to simplify an equation, or you might be trying to get an unknown to one side of the equation to solve for it. Let's start by looking at the following equation.

*a = b * c*

Let's try to get 'b' by itself on the right side of the equal sign. So we need to get rid of that 'c.' We can do this by dividing the right side of the equation by another 'c.'

*a = b * c / c*

Even though we don't know what number 'c' is, we know that any number divided by itself equals one. So:

*c / c = 1*

Therefore, we get:

*a = b * 1*

Also, every number multiplied by one equals itself.

*b * 1 = b*

So our original equation is now the following.

*a = b*

However, right now this equation is incorrect. When we perform an operation to one side of the equal sign, we must also perform that same operation to the other side in order for the equation to stay true. This is necessary when performing any of the math operations. So we must divide the left side of the equal sign by 'c,' just like we did to the right. We get:

*a / c = b*

Now we have the correct rearranged equation with 'b' by itself on the right side of the equal sign.

In physics, we often work with polynomials. A **polynomial** is a math equation with multiple terms. For example, the polynomial *a - b* has the two terms of 'a' and 'b.'

Two of the most common rules for dealing with polynomials you will have to know are the distributive law and how to multiply them together.

The **distributive law** tells us how to multiply or divide a polynomial by a single number or variable. We do this by the following method.

*a * (b + c) = ab + ac*

or

*(b + c) / a = b/a + c/a*

The distributive law can also be done in reverse if we notice a common number or variable between terms in an equation. For instance:

*ab + ac + d = a * (b + c) + d*

Note that the 'd' isn't added to the parentheses because it didn't have an 'a' multiplied by it.

Now that we know how to multiply a polynomial by a single number or variable, let's look at how we multiply two polynomials together. Let's try and multiply two polynomials together in the following equation.

*(a + 2)(c + 3) = ?*

To multiply these two together we multiply the second polynomial by 'a' from the first plus the second polynomial again by the 2 from the first. In other words:

*(a + 2)(c + 3) = a * (c + 3) + 2 * (c + 3)*

We then use the distributive law to multiply the 'a' and 2 into the polynomials they are each next to. So:

*(a + 2)(c + 3) = ac + 3a + 2c + 6*

Another thing we work with a lot in physics courses are exponents. There are a multitude of useful rules that relate to exponents. Let's quickly go over them.

The **zero rule** states that any number raised to a power of zero is always equal to 1.

There are two **one rules**. The first shows that much like the zero rule, the number 1 raised to whatever power is always equal to 1.

The second states that a number raised to the first power is always equal to itself.

The **negative rule** explains how we can reform a negative exponent as a positive one by writing the number it is being raised to as a reciprocal. In other words, a number raised to a negative power is equal to one divided by that number raised to a positive power of the same magnitude.

The **product rule** shows us how two equal numbers with different exponents multiplied together is equal to that number raised to the addition of the two exponents.

Similarly, the **quotient rule** tells us that two equal numbers with different exponents being divided together is equal to that number raised to the subtraction of the two exponents.

Finally, the **power rule** explains that when we have an exponent raised to another exponent this is the same as having the two exponents multiplied together.

In a physics course there are many math techniques you will have to know to be successful. Three things you will need to know how to do are rearrange equations, work with polynomials, and manipulate exponents.

When you are rearranging an equation, any operation you perform on one side of the equal sign must also be performed on the other. For example, to get 'b' by itself in the equation on screen we need to multiply both sides of the equation by 'c.'

A **polynomial** is a math equation with multiple terms, and the **distributive law** tells us how to multiply or divide a polynomial by a single number or variable.

We can also multiply polynomials together. In the first step we get a series of terms of one number multiplied by a polynomial added or subtracted together. We then finish multiplying these individual terms out by using the distributive law.

There are a few rules regarding exponents that you will need to know.

The **zero rule** states that any number raised to the power of zero is always equal to 1.

The **one rules** show that both the number one raised to a power is always equal to one, and that a number raised to the first power equals itself.

The **negative rule** explains that a number raised to a negative power is equal to one divided by that number raised to a positive power of the same magnitude.

The **product rule** shows us how two equal numbers with different exponents multiplied together is equal to that number raised to the addition of the two exponents.

The **quotient rule** tells us that two equal numbers with different exponents being divided together is equal to that number raised to the subtraction of the two exponents.

Finally, the **power rule** explains that when we have an exponent raised to another exponent this is the same as having the two exponents multiplied together.

When you are finished, you should be able to:

- Recall some of the algebra concepts needed for physics courses
- Solve a math equation involving rearranging, the distributive property, or polynomials
- State the rules for working with exponents

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Physics: High School18 chapters | 212 lessons

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