Algebraic ExpressionsLet"s gain down come business. An expression is consisted of of terms. Terms room the separate values in an expression. Every term can be a variable, a number and a variable, or a number and many variables through or without exponents, as long as whatever is gift multiplied with each other in a solitary nugget of mathematics goodness. Few of our favourite terms include:
These all count as a single term.
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A number alongside a variable means that number and also variable room being multiplied. The same is true for 2 variables alongside each other: it method they"re being multiplied. Because the × we used for multiplication in the past looks an awful lot like the variable x, we"ll prevent using a symbol for multiplication in ~ all. Some speak to it lazy; we speak to it efficient.
Some terms space numbers only. This are dubbed constants, or numbers that don"t change. Others have actually variables (letters that stand for an unknown or transforming number), and also some have variables and also numbers mashed together, in which situation the numbers are called coefficients.
Occasionally terms, like the last one above, seem to be absent a coefficient. Here"s the thing: they in reality do have actually a coefficient that 1. It"s just too lazy to display up. Because 1 time anything is just that anything, we generally don"t compose 1 together a coefficient, however it"s always there.
Example: x is the same thing together 1x, and x3y2m is the same thing as 1x3y2m.
Variable: one unknown or transforming number. Often represented by x.Constant: a number that doesn"t change.Coefficient: the number that"s multiply by the variable.
We like terms, and we specifically like like terms. Like terms are terms that have actually the very same variables, consisting of the exponents that go v those variables. The variables can be in various orders and also have various coefficients, but they all need to be there.
Examples:3xy and also -5xy are favor terms (same variables).3xy and also -5xym are not prefer terms (the 2nd term has a variable that the very first doesn"t).
-2m2xh and also 4m2hx are choose terms (same variables and also exponents, just in different order).-2m3xh and 4m2xh are not like terms (the variable m has different exponents in each term).
If there"s much more than one term separated by to add or minus signs, climate we have actually an expression. Because that example:
5x2y – 3xy + y + 5
This expression has 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 usual phrases.
|plusaddsummore thanin enhancement togreater thantotal and||differencesubtractless thantake away||productoftimestwice (×2)factor||divided byquotientsplitsharedistribute||is|
In this translations, we"ll use the letter x to represent the variable, though any letter, symbol, or emoticon would certainly work. Smiley faces and hearts, anyone?
|a number enhanced by twelve||x + 12|
|the amount of twice a number and six||2x + 6|
|eighty much less than a number||x – 80|
|twenty-eight break-up in half||28 ÷ 2|
|the product the a number and seven||7x|
|the quotient the 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 complete of forty and also a number||40 + x|
|three times the total of a number and five||3(x + 5)|
|A number is an adverse ten.||x = -10|
|A number plus 2 is eight.||x + 2 = 8|
|The difference in between a number and seven is an adverse three.||x – 7 = -3|
|One less than twice a number is seventeen.||2x – 1 = 17|
|Twelve is the product that a number and three.||12 = 3x|
|Half the a number is twenty.|
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|½x = 20|
|A number is same to the amount of twice the number and an unfavorable three.||x = 2x + (-3)|
Look Out: be really careful through "less than." Three less than a number is translated as "x – 3." The reverse of that, "3 – x," would certainly be a number less than 3.