Identifying "Like" terms.

[Norloonda]

The book I'm reading gives limited information then illustrates what to do in combining "Like terms". My question is do signs (-/+) make a difference on whether terms are "Like" or not. I'm not sure if the framers of this area is looking at "absolute value".

Example:

A. While these are "Like Terms" A1. 3a^mbⁿ + 7a^mbⁿ A2. 2c^gd^h + 9c^gd^h A3. 1.5b^ec^m + 25b^ec^m.

B. Are these "Like Terms"? B1. 3a^mbⁿ + 7a^m(-bⁿ⁾ B2. (-2-c^gd^h + 9c^g-d^h B3. 1.5b^ec^m + (-25b^e)c^m


C. Are these "Like Terms" if the sequence of variables with there respective exponents were switched? C1. 3a^mbⁿ + 7bⁿa^m C2. 2c^gd^h + 9d^hc^g etc....

 

[Deleted member 4993]

The book I'm reading gives limited information then illustrates what to do in combining "Like terms". My question is do signs (-/+) make a difference on whether terms are "Like" or not. I'm not sure if the framers of this area is looking at "absolute value".

Example:

A. While these are "Like Terms" A1. 3a^mbⁿ + 7a^mbⁿ .............A2. 2c^gd^h + 9c^gd^h ..................A3. 1.5b^ec^m + 25b^ec^m.

B. Are these "Like Terms"? B1. 3a^mbⁿ + 7a^m(-bⁿ⁾ ................B2. (-2)(-c^g)d^h + 9c^g(-d^h).............B3. 1.5b^ec^m + (-25)(b^e)c^m Yes to all (with grouping symbols as shown)

You can add or subtract those terms. The answer of addition/subtraction will depend on whether the exponent is "odd" or "even"

C. Are these "Like Terms" if the sequence of variables with there respective exponents were switched? C1. 3a^mbⁿ + 7bⁿa^m ..........C2. 2c^gd^h + 9d^hc^g etc....

Yes ... because scalar multiplication is commutative.

.

 

[HallsofIvy]

Does your book, before defining "combining like terms", not define "like terms"? That would be very strange!

 

[Norloonda]

Book definition

Does your book, before defining "combining like terms", not define "like terms"? That would be very strange!

Yes

My book defines "like terms" as terms that have matching variables and exponents.

 

[Norloonda]

.

Very Grateful "Thanks".

 

[HallsofIvy]

Yes

My book defines "like terms" as terms that have matching variables and exponents.

So the coefficients have no part in determining "like terms". In particular whether the coefficients are positive or negative does not matter.