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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: understand the concept of like terms, be able to combine like terms, be able to simplify expressions containing parentheses.

Overview

  • Like Terms
  • Combining Like Terms
  • Simplifying Expressions Containing Parentheses

Like terms

Like terms

Terms whose variable parts, including the exponents, are identical are called like terms . Like terms is an appropriate name since terms with identical variable parts and different numerical coefficients represent different amounts of the same quantity. As long as we are dealing with quantities of the same type we can combine them using addition and subtraction.

Simplifying an algebraic expression

An algebraic expression can be simplified by combining like terms.

Sample set a

Combine the like terms.

6 houses + 4 houses = 10 houses . 6 and 4 of the same type give 10 of that type.

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6 houses + 4 houses + 2 motels = 10 houses + 2 motels . 6 and 4 of the same type give 10 of that type. Thus, we have 10 of one type and 2 of another type.

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Suppose we let the letter x represent "house." Then, 6 x + 4 x = 10 x . 6 and 4 of the same type give 10 of that type.

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Suppose we let x represent "house" and y represent "motel."

6 x + 4 x + 2 y = 10 x + 2 y

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Practice set a

Like terms with the same numerical coefficient represent equal amounts of the same quantity.

Like terms with different numerical coefficients represent .

different amounts of the same quantity

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Combining like terms

Since like terms represent amounts of the same quantity, they may be combined, that is, like terms may be added together.

Sample set b

Simplify each of the following polynomials by combining like terms.

2 x + 5 x + 3 x .
There are 2 x ' s , then 5 more, then 3 more. This makes a total of 10 x ' s .

2 x + 5 x + 3 x = 10 x

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7 x + 8 y 3 x .
From 7 x ' s , we lose 3 x ' s . This makes 4 x ' s . The 8 y ' s represent a quantity different from the x ' s and therefore will not combine with them.

7 x + 8 y 3 x = 4 x + 8 y

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4 a 3 2 a 2 + 8 a 3 + a 2 2 a 3 .
4 a 3 , 8 a 3 , and 2 a 3 represent quantities of the same type.

4 a 3 + 8 a 3 2 a 3 = 10 a 3

2 a 2 and a 2 represent quantities of the same type.

2 a 2 + a 2 = a 2

Thus,

4 a 3 2 a 2 + 8 a 3 + a 2 2 a 3 = 10 a 3 a 2

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Practice set b

Simplify each of the following expressions.

5 a + 2 b + 4 a b 7 b

9 a 6 b

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10 x 3 4 x 3 + 3 x 2 12 x 3 + 5 x 2 + 2 x + x 3 + 8 x

5 x 3 + 8 x 2 + 10 x

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2 a 5 a 5 + 1 4 a b 9 + 9 a b 2 3 a 5

5 a b 13

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Simplifying expressions containing parentheses

Simplifying expressions containing parentheses

When parentheses occur in expressions, they must be removed before the expression can be simplified. Parentheses can be removed using the distributive property.

Distributive property

The product of a monomial a and a binomial b plus c is equal to ab plus ac. This is the distributive property. In the expression, there are two arrows originating from the monomial, a, and pointing towards the terms b and c of the binomial.

Sample set c

Simplify each of the following expressions by using the distributive property and combining like terms.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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