like terms

Examples of like terms in the following topics:

• Adding and Subtracting Polynomials

  • For example, $4x^3$ and $x^3$are like terms; $21$ and $82$ are also like terms.
  • When adding polynomials, the commutative property allows us to rearrange the terms to group like terms together.
  • For example, one polynomial may have the term $x^2$, while the other polynomial has no like term.
  • If any term does not have a like term in the other polynomial, it does not need to be combined with any other term.
  • Start by grouping like terms.

• Adding and Subtracting Algebraic Expressions

  • Terms are called like terms if they involve the same variables and exponents.
  • All constants are also like terms.
  • Likewise, the following are examples of like terms:
  • Now group these like terms together:
  • Now group these like terms together:

• Sums, Differences, Products, and Quotients

  • In adding equations, it is important to collect like terms to simplify the expression.
  • "Like terms" are those that have the same kind of variable.
  • We then collect like terms.
  • In this case, "x" and "2x" are like terms, as are "5" and "-3. " The result is:
  • It is important to remember to only add together like terms.

• Multiplying Algebraic Expressions

  • (Note that multiplying monomials is not the same as adding algebraic expressions—monomials do not have to involve "like terms" in order to be combined together through multiplication.)
  • Outer (the "outside" terms are multiplied—i.e., the first term of the first binomial with the second term of the second)
  • Inner (the "inside" terms are multiplied—i.e., the second term of the first binomial with the first term of the second)
  • Additionally, remember to simplify the resulting polynomial if possible by combining like terms.
  • Notice that two of these terms are like terms ($-4x$ and $3x$) and can therefore be added together to simplify the expression further:

• Introduction

  • The three components of the IP model is the sensory receptor (SR), short-term memory (STM), and long-term memory (LTM).
  • Information is moved from the sensory receptor to short-term memory and compared to information stored in the long-term memory.
  • Caption: The illustration above represents my coffee cup example.Light reflects off the cup and into the eye.The image is then transferred through the optic nerve to the sensory register.From the sensory register, the image is moved into Short-term Memory (STM) as information about the cup is drawn from Long-term Memory (LTM).The process of elaboration occurs when information is retrieved from the LTM in order to link to the new information.I would like to thank Liyan Song for her work on the Flash model shown above.
  • The Sensory Register would include input devices like CDs.
  • Short Term Memory includes the Central Processing Unit.

• Short-Term and Working Memory

  • Though the term "working memory" is often used synonymously with "short-term memory," working memory is related to but actually distinct from short-term memory.
  • It also links the working memory to the long-term memory, controls the storage of long-term memory, and manages memory retrieval from storage.
  • The process of transferring information from short-term to long-term memory involves encoding and consolidation of information.
  • This is a function of time; that is, the longer the memory stays in the short-term memory the more likely it is to be placed in the long-term memory.
  • The limbic system of the brain (including the hippocampus and amygdala) is not necessarily directly involved in long-term memory, but it selects particular information from short-term memory and consolidates these memories by playing them like a continuous tape.

• Summing Terms in an Arithmetic Sequence

  • First we think of it as the sum of terms that are written in terms of $a_1$, so that the second term is $a_1+d$, the third is $a_1+2d$, and so on.
  • Then our sum looks like:
  • Next, we think of each term as being written in terms of the last term, $a_n$.
  • Then the last term is $a_n$, the term before the last is $a_n-d$, the term before that is $a_n-2d$, and so on.
  • An infinite arithmetic series is exactly what it sounds like: an infinite series whose terms are in an arithmetic sequence.

• The General Term of a Sequence

  • Given several terms in a sequence, it is sometimes possible to find a formula for the general term of the sequence.
  • Then the sequence looks like:
  • The difference between each term and the term after it is $a$.
  • Then the sequence would look like:
  • If we start at the second term, and subtract the previous term from each term in the sequence, we can get a new sequence made up of the differences between terms.

• Long-Term Approach

  • Current liabilities are debts owed in the short term, such as accounts payable, short-term debts, and other obligations within a short operational cycle.
  • While short-term planning is predominately what is used in respect to working capital (due to the short term nature of the inputs and outputs involved), it is reasonable to set long-term polices and strategies for incorporating changes in working capital into financial strategy.
  • From a strategic perspective, there is a certain amount of liquidity business would like to maintain at any given moment to ensure that they can capture external opportunities in the market.
  • From the long-term perspective, this profitability metric will be quite a bit different than the short term.
  • Despite the potential advantages of longer-term planning in working capital, it is still largely a field of shorter term decision making.

• Capacity Planning

  • " in both long-term and short-term situations.
  • Determining the organization's capacity to produce goods and services involves both long-term and short-term decisions.
  • Long-term capacity decisions involve facilities and major equipment investments .
  • Buying a large single airplane like the Super Jumbo Jet may not be the right capacity decision for an airline that serves numerous medium-sized cities.
  • Capacity decisions are also required in short-term situations.