Algebraic ExpressionsLet"s acquire down to business. An expression is consisted of of terms. Terms are the separate values in an expression. Each term have the right to be a variable, a number and also a variable, or a number and also many kind of variables through or without exponents, as lengthy as whatever is being multiplied together in a single nuggain of math goodness. Some of our favorite terms include:
These all count as a single term.
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A number beside a variable indicates that number and variable are being multiplied. The exact same is true for two variables next to each other: it implies they"re being multiplied. Due to the fact that the × we offered for multiplication in the previous looks an awful lot favor the variable x, we"ll soptimal making use of a symbol for multiplication at all. Some call it lazy; we contact it effective.
Some terms are numbers just. These are referred to as constants, or numbers that don"t change. Others have actually variables (letters that reexisting an unwell-known or altering number), and also some have actually variables and numbers mamelted together, in which situation the numbers are referred to as coefficients.
Occasionally terms, choose the last one above, seem to be lacking a coreliable. Here"s the thing: they actually execute have a coreliable of 1. It"s just also lazy to present up. Since 1 times anypoint is just that anything, we normally do not write 1 as a coreliable, but it"s always tbelow.
Example: x is the very same point as 1x, and x3y2m is the very same thing as 1x3y2m.
Variable: an unrecognized or altering number. Often stood for by x.Constant: a number that does not change.Coefficient: the number that"s multiplied by the variable.
We choose terms, and also we particularly like like terms. Like terms are terms that have the very same variables, consisting of the exponents that go with those variables. The variables can be in different orders and also have actually different coefficients, yet they all need to be tright here.
Examples:3xy and -5xy are prefer terms (very same variables).3xy and -5xym are not choose terms (the second term has actually a variable that the first doesn"t).
-2m2xh and also 4m2hx are like terms (very same variables and exponents, just in various order).-2m3xh and also 4m2xh are not prefer terms (the variable m has different exponents in each term).
If there"s even more than one term separated by plus or minus indicators, then we have actually an expression. For example:
5x2y – 3xy + y + 5
This expression has actually four terms: 5x2y, -3xy, y (or 1y), and 5.
Names for algebraic expressions
|binomial||2 Terms||xy – 2x|
|trinomial||3 Terms||xy – 2x + 3y|
|quadnomial||4 Terms||xy – 2x + 3y – 1|
Here is a chart of widespread phrases.
|plusaddsummore thanin addition tobetter thanfull and||differencesubtractmuch less thantake ameans||productoftimestwice (×2)factor||split byquotientsplitsharedistribute||is|
In these translations, we"ll use the letter x to represent the variable, though any kind of letter, symbol, or emoticon would certainly work. Smiley faces and hearts, anyone?
|a number raised by twelve||x + 12|
|the amount of twice a number and six||2x + 6|
|eighty much less than a number||x – 80|
|twenty-eight split in half||28 ÷ 2|
|the product of a number and seven||7x|
|the quotient of a number and also four||x ÷ 4|
|five better than three times a number||3x + 5|
|a number spread evenly among six||x ÷ 6|
|the full of forty and also a number||40 + x|
|3 times the total of a number and five||3(x + 5)|
|A number is negative ten.||x = -10|
|A number plus two is eight.||x + 2 = 8|
|The difference in between a number and seven is negative 3.||x – 7 = -3|
|One much less than twice a number is seventeenager.||2x – 1 = 17|
|Twelve is the product of a number and three.||12 = 3x|
|Half of a number is twenty.|
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|½x = 20|
|A number is equal to the amount of twice the number and negative three.||x = 2x + (-3)|
Look Out: be extremely careful with "less than." Three much less than a number is translated as "x – 3." The reverse of that, "3 – x," would be a number less than 3.