Transcript 2.6 Simplifying Expressions
Simplifying Algebraic Expressions
Distribution and Like Terms Section 4.2
Notes When a ________ or ________ sign separates an algebraic expression into parts, each part is called a _______.
The numerical factor of a term that contains a variable is called the ____________.
Notes A term without a variable is called a _________.
__________ terms contain the same variables to the same powers, such as 3x and 2x.
Like Terms Like Terms have the EXACT same variables with the same exponents.
Like Terms 2x, -5x -8, 10 3y ², 8y² 7xy, -xy Unlike Terms 4x, 4y 9, 6x 5x, 5x² 3x²y, 8xy²
Examples Identify the terms, like terms, coefficients, and constants 1. 4 – 4y + y – 3 2. 7 – 5y + 2 + 1
Example
Find the like terms: 7x, -8, 4y, x, x ², 6, 5xy, 8y, 9
Notes An algebraic expression is in _____________form if it has no like terms and no parentheses.
Combining Like Terms
Terms must be
like
in order to add and subtract them.
To combine like terms:
Add
the coefficients Keep the variable
Examples
6x + 5y – 3x + y -2x – 8y + 5x – 4y 5a – 2b + c – 5b + 4b
Distributive Property
Signified by a number next to ( ) with no sign in between Ex: 5(x + 3) Tells you to multiply the number outside by every term inside Watch the signs
4(x + 3) (2y – 6)5 a(7b + 2c) -8(4m – 2n)
Examples
Simplifying Expressions o Distribute first (watch for sign of # you are distributing) o Combine like terms
Examples
3(x + 2) – 4x + 8 2 – 5(2x + 4) + x 2(3x – 4y) – (x – 2y)