How do you combine like terms in #(5x^2+4)-(3x+7)+(2x^2-1)#?

1 Answer
Mar 24, 2018

Answer:

#7x^2 - 3x - 4#

Explanation:

Like terms are defined as terms with the same variables that are raised to the same power.

For example, the terms #ax# and #bx^2# are NOT like terms because the coefficients #a# and #b# have variables (#x# and #x^2#, respectively) that are not raised to the same power.

In the expression #(5x^2+4)-(3x+7)+(2x^2-1)#, the like terms are grouped as follows:
#5x^2# and #2x^2#

#-3x# (this is negative because the subtraction sign is "distributed" to the terms inside of the parentheses)

#4#, #-7#, #-1# (the reason for why it's #-7# is the same reason for why #-3x# is negative)

Add the terms in the groups up...
#5x^2 + 2x^2 = 7x^2#
#-3x#
#4 - 7 - 1 = -4#

Now you have the simplified expression: #7x^2 - 3x - 4#