Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match EXAMPLES : - Like terms, can be combined - Can NOT be combined, exponents are different.. - Can NOT be combined, two totally different terms - Like terms, can be combined

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “ EXAMPLES : Term DOES NOT change !!!

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “ EXAMPLES : Term DOES NOT change !!! ONLY combine the coefficients !!!

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “ c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets. EXAMPLE : It is just like you are multiplying ( - 1 ) by everything inside…

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “ c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets. d ) when a positive sign appears in front of a set of parentheses or brackets, just drop the parentheses or brackets and keep the signs the terms already hold. EXAMPLE :

Simplifying Algebraic Expressions RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like terms “ c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets. d ) when a positive sign appears in front of a set of parentheses or brackets, just drop the parentheses or brackets and keep the signs the terms already hold. e ) when multiple parentheses and brackets are used, work from the INNER most bracket out

Simplifying Algebraic Expressions EXAMPLE 1 :

Simplifying Algebraic Expressions EXAMPLE 1 : I like to draw little “walls” in between each term so I can see them better

Simplifying Algebraic Expressions EXAMPLE 1 : Next, make a list of the terms you see…and find the matches, combine coefficients.

Simplifying Algebraic Expressions EXAMPLE 1 : Next, make a list of the terms you see…and find the matches, combine coefficients.

Simplifying Algebraic Expressions EXAMPLE 1 : Next, make a list of the terms you see…and find the matches, combine coefficients. I’ll also cross out the ones I just used… it helps you see “what’s left”…

Simplifying Algebraic Expressions EXAMPLE 1 : Next, make a list of the terms you see…and find the matches, combine coefficients.

Simplifying Algebraic Expressions EXAMPLE 1 : Looks like we got all of them.

Simplifying Algebraic Expressions EXAMPLE 1 : Your answer is right here...

Simplifying Algebraic Expressions EXAMPLE 1 : Your answer is right here...

Simplifying Algebraic Expressions EXAMPLE 2 :

Simplifying Algebraic Expressions EXAMPLE 2 : OK, we have brackets and imbedded parens here. So again, we will work with the inner most parens first.

Simplifying Algebraic Expressions EXAMPLE 2 : Drop brackets and signs stay the same Change signs in set 1

Simplifying Algebraic Expressions EXAMPLE 2 : Combine like terms inside both brackets

Simplifying Algebraic Expressions EXAMPLE 2 : Drop brackets and change signs

Simplifying Algebraic Expressions EXAMPLE 2 : Separate your terms

Simplifying Algebraic Expressions EXAMPLE 2 : ANSWER

Simplifying Algebraic Expressions EXAMPLE 3 :

Simplifying Algebraic Expressions EXAMPLE 3 : OK, multiple imbedded brackets / parens. Start with the innermost set…

Simplifying Algebraic Expressions EXAMPLE 3 : Drop parens and change signs

Simplifying Algebraic Expressions EXAMPLE 3 : Combine like terms inside brackets

Simplifying Algebraic Expressions EXAMPLE 3 : Drop brackets and keep signs

Simplifying Algebraic Expressions EXAMPLE 3 : Combine like terms inside

Simplifying Algebraic Expressions EXAMPLE 3 : Drop brackets and change signs

Simplifying Algebraic Expressions EXAMPLE 3 : Combine like terms

Simplifying Algebraic Expressions EXAMPLE 3 : ANSWER