## Algebraic Expressions

Let"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:

77*x*7*x*2*y**x*6*y*11*z*2

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 1*x*, and *x*3*y*2*m* is the same thing as 1*x*3*y*2*m*.

**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:**3*xy* and also -5*xy* **are** favor terms (same variables).3*xy* and also -5*xym* **are not** prefer terms (the 2nd term has a variable that the very first doesn"t).

-2*m*2*xh* and also 4*m*2*hx* **are** choose terms (same variables and also exponents, just in different order).-2*m*3*xh* and 4*m*2*xh* **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:

5*x*2*y* – 3*xy* + *y* + 5

This expression has four terms: 5*x*2*y*, -3*xy*, *y* (or 1*y*), and 5.

### Names for algebraic expressions

monomial | 1 Term | xy |

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.

Common Words and also Phrases for:AddSubtractMultiplyDivideEqualsplusaddsummore 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. See more: Matter In Crystalline Solids The Particles Are Not Arranged In A Regular Pattern | 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.