7-1 Multiplying Monomials

Chapter 7 is over polynomials. Polynomials are expressions involving numbers and variables which represent the world around us. The Biblical worldview of polynomials is the same as that of expressions, equations, and inequalities...

It is important to keep this broad perspective as we delve into the nuts and bolts of polynomials, beginning today with monomials.

A polynomial is a many-termed expression (it can have one, two, or several terms). A monomial is an expression with only one term. It can be a ___________, a _____________, or the ____________ of a number and one or more variables. Any exponents must be ______________ integers, and there can be no variables in the ________________.

Look at Check Your Understanding pg. 404, numbers 1-6. Which of these are NOT monomials?

________ Why not? ________ Why not? _________ Why not?

All of the others fit the above definition of a monomial.

Simplifying expressions - Until now, simplifying has meant mainly distributing multiplication where necessary and combining any like terms. Now there will be more things to simplify, namely monomials to be multiplied. In general though, simplifying always means ʻwhatever operation can be done, do itʼ. The key concept box on pg. 404 tells you what to look for to know that a monomial expression is simplified. You can use this checklist if you want, but itʼs better to just recognize outstanding multiplication when you see it.

Numbers 7-15 in the CYU pg. 404 say to ʻsimplify each expressionʼ. These are all like examples 2 and 3 in your book, where monomials are being multiplied or raised to a power.

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You can remember the ʻrulesʼ of multiplying monomials from prealgebra:

# * When you multiply ʻlikeʼ bases, you ______ exponents.

# # (Product of Powers) (xm)(xn) = xm+n

# * When you raise a power to a power, you ___________ exponents.

# # (Power of a Power)# (x m)n = xmn

Because the Lord was orderly in His creation, we can use mathematical tools such as polynomials to represent the relationships that exist around us in the world, enabling us to more efficiently exist in and cooperate with (have dominion over) the earth that He gave to us.

OR you can simply reason it out... # 7.)

And remember to apply the exponent to each factor! (Power of a Product) (xy)m = xmym

# 12.)

Letʼs take a look at one like #15.

To keep everything orderly and not lose track, it is good to show your steps and apply the power to each FACTOR, like this:

You can do this in your head, but be careful!Like example 4: # 16.)

Like example 5: (Remember to use PEMDAS!....apply exponents before multiplying)

# 17.)

# 18.)

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Problems for Practice: 29, 33, 37, 43 **Shortened from video!! (All answers should be checked as correct with a colored check, if you got them correct the first time. OR they should be marked as incorrect with a colored mark and then corrected to the side. Use Hotmath if necessary.)

Skills/Spiral Review: 75, 84 (by hand, no calculator)

Opportunity for HW 7-1 exemption: #54, 56**If youʼve completed the problems for practice and skills/spiral review, and if you get these next two problems correct the first time with no help from any person, then you are exempt from HW 7-1, and you get bonus points for these problems.**

Show all steps here:54.) # # # # # # 56.)

BIBLICAL INTEGRATION: The heavens declare the glory of God, and the firmament shows His handiwork. The visible things that we are able to study reveal to us invisible truths. Everything revealed by creation will and can only verify the Truth that we see in His Word. Science cannot refute scripture; if it seems to do so, then it's because either our knowledge of science or of the Word is in part or incorrect. Einstein's famous formula E=mc² is a great example of this.

Read the caption under Albert Einstein on page 406. Imagine if you were able to take a physical object, say a blade of grass, and throw it at the speed of light, squared. Visualize it turning into energy.

Now, take the formula E=mc² and solve for m. This now says that mass m is energy E, divided by (or slowed down) by the speed of light, squared. Ie, the reverse of what you just visualized. Imagine it in reverse...the energy slowing down and forming the blade of grass. Is there anything in scripture that could back up this possibility? Think about how the earth was formed. (by the spoken Word of God). God said 'Let there be', and it was. And scripture says that everything is 'held together by the Word of God'. Is there anything in science that demonstrates this? Indeed, science says that all matter is in motion, made up of quarks, or...vibrations. Thatʼs what sound is...vibrations. So God spoke and the physical world was formed. And thousands of years later that very matter is found to still be vibrating at the molecular level.

“How precious are your thoughts, Oh God. How vast is the sum of them!” Ps 139:17

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