Algebraic expressions room combinations that variables , numbers, and also at least one arithmetic operation.

for example, 2 x + 4 y − 9 is an algebraic expression.

** Term: ** each expression is consisted of of terms. A term can be a signed number, a variable, or a consistent multiplied by a change or variables.

** Factor: ** Something i m sorry is multiplied by something else. A variable can it is in a number, variable, term, or a longer expression. For example, the expression 7 x ( y + 3 ) has actually three factors: 7 , x , and also ( y + 3 ) .

** Coefficient: ** The numerical element of a multiplication expression that consists of a variable. Think about the expression in the number above, 2 x + 4 y − 9 . In the an initial term, 2 x , the coefficient is 2 : in the 2nd term, 4 y , the coefficient is 4 .

** Constant: ** A number that cannot change its value. In the expression 2 x + 4 y − 9 , the term 9 is a constant.

** prefer Terms: ** Terms that contain the exact same variables such as 2 m , 6 m or 3 x y and also 7 x y . If an expression has more than one consistent terms, those are likewise like terms.

Expression | indigenous Phrases |

n + 5 | amount of a number and 5 |

m − 7 | difference of a number and also 7 |

6 x | Product of 6 and a number |

y ÷ 9 | Quotient the a number and 9 |

You are watching: A combination of variables, numbers and at least one operation

** Example: **

recognize the terms, choose terms, coefficients, and also constants in the expression.

9 m − 5 n + 2 + m − 7

First, we can rewrite the subtractions together additions.

9 m − 5 n + 2 + m − 7 = 9 m + ( − 5 n ) + 2 + m + ( − 7 )

So, the ** state ** are 9 m , ( − 5 n ) , m , 2 , and also ( − 7 ) .

** like terms ** space terms that contain the same variables.

9 m and also 9 m room a pair of ** like terms ** . The continuous terms 2 and − 7 are also like terms.

** Coefficients ** space the numerical parts of a ax that contains a variable.

So, right here the ** coefficients ** room 9 , ( − 5 ) , and also 1 . ( 1 is the coefficient that the term m .)

The ** continuous ** terms space the terms with no variables, in this case 2 and also − 7 .

Algebraic expressions need to be written and also interpreted carefully. The algebraic expression 5 ( x + 9 ) is ** no ** indistinguishable to the algebraic expression, 5 x + 9 .

check out the difference between the two expressions in the table below.

indigenous Phrases | Algebraic Expression |

five times the amount of a number and nine | 5 ( x + 9 ) |

Nine an ext than five times a number | 5 x + 9 |

In creating expressions for unknown quantities, we frequently use typical formulas. For example, the algebraic expression for "the distance if the rate is 50 miles per hour and the time is T hours" is D = 50 T (using the formula D = R T ).

an expression prefer x n is dubbed a power. Here x is the base, and also n is the exponent. The exponent is the number of times the basic is provided as a factor. The word expression for this expression is " x come the n th power."

right here are some of the instances of using exponents.

word Phrases | Algebraic Expression |

seven times m come the fourth power | 7 m 4 |

The sum of x squared and 12 times of y | x 2 + 12 y |

x cubed times y come the 6th power | See more: How Many Day Till Christmas 2017 ? How Many Days Are Left Until Christmas 2017 x 3 ⋅ y 6 |