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Simplify each algebraic expression.

  1. 2 3 y 2 ( 4 3 y + z )
  2. 5 t 2 3 t + 1
  3. 4 p ( q 1 ) + q ( 1 p )
  4. 9 r ( s + 2 r ) + ( 6 s )
  1. −2 y −2 z  or  −2 ( y + z ) ;
  2. 2 t −1 ;
  3. 3 p q −4 p + q ;
  4. 7 r −2 s + 6
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Simplifying a formula

A rectangle with length L and width W has a perimeter P given by P = L + W + L + W . Simplify this expression.

P = L + W + L + W P = L + L + W + W Commutative property of addition P = 2 L + 2 W Simplify P = 2 ( L + W ) Distributive property
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If the amount P is deposited into an account paying simple interest r for time t , the total value of the deposit A is given by A = P + P r t . Simplify the expression. (This formula will be explored in more detail later in the course.)

A = P ( 1 + r t )

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Access these online resources for additional instruction and practice with real numbers.

Key concepts

  • Rational numbers may be written as fractions or terminating or repeating decimals. See [link] and [link] .
  • Determine whether a number is rational or irrational by writing it as a decimal. See [link] .
  • The rational numbers and irrational numbers make up the set of real numbers. See [link] . A number can be classified as natural, whole, integer, rational, or irrational. See [link] .
  • The order of operations is used to evaluate expressions. See [link] .
  • The real numbers under the operations of addition and multiplication obey basic rules, known as the properties of real numbers. These are the commutative properties, the associative properties, the distributive property, the identity properties, and the inverse properties. See [link] .
  • Algebraic expressions are composed of constants and variables that are combined using addition, subtraction, multiplication, and division. See [link] . They take on a numerical value when evaluated by replacing variables with constants. See [link] , [link] , and [link]
  • Formulas are equations in which one quantity is represented in terms of other quantities. They may be simplified or evaluated as any mathematical expression. See [link] and [link] .

Verbal

Is 2 an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

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What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?

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What do the Associative Properties allow us to do when following the order of operations? Explain your answer.

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

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Numeric

For the following exercises, simplify the given expression.

10 + 2 × ( 5 3 )

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6 ÷ 2 ( 81 ÷ 3 2 )

−6

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−2 × [ 16 ÷ ( 8 4 ) 2 ] 2

−2

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4 6 + 2 × 7

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3 12 × 2 + 19

-2

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14 × 3 ÷ 7 6

0

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9 ( 3 + 11 ) × 2

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6 + 2 × 2 1

9

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64 ÷ ( 8 + 4 × 2 )

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( 12 ÷ 3 × 3 ) 2

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( 15 7 ) × ( 3 7 )

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2 × 4 9 ( −1 )

17

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4 2 25 × 1 5

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Algebraic

For the following exercises, solve for the variable.

Questions & Answers

How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
v=lbh calculate the volume if i.l=5cm, b=2cm ,h=3cm
Haidar Reply
Need help with math
Peya
can you help me on this topic of Geometry if l help you
litshani
( cosec Q _ cot Q ) whole spuare = 1_cosQ / 1+cosQ
Aarav Reply
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?
Maxwell Reply
the indicated sum of a sequence is known as
Arku Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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