How do you subtract #(1.5x ^ { 3} + 4.2x ^ { 2} - 37x ) - ( - 4.8x ^ { 3} - 42x ^ { 2} + 89)#?

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Answer 1 · 2016-12-27T10:33:01

#6.3x^3+46.2x^2-37x-89#

For multiply and divide: when the signs are different the answer is negative but when the signs are the same the answer is positive.

so #3-(-2)# process is:
change the sign of the 2 #->3+2=5#

#color(white)(.)#

so #3-(+2)# process is:
change the sign of the 2 #->3-2=1#

#color(white)(.)#

so #3+(+2)# process is:
don't change the sign of the 2 #->3+2=5#

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#color(blue)("Answering the question")#

Consider: #-(-4.8x^3-42x^2+89) #

This is the same as:# (-1)xx(-4.8x^3-42x^2+89)#

So we change the sign of everything inside the brackets.

Which gives:#" "+4.8x^3+42x^2-89#

#color(brown)("Putting it all together")#

#1.5x^3+4.2x^2-37x+0 larr" The 0 is just a place keeper"#
#ul(+4.8x^3+42x^2+0x-89) larr" The "0x" is just a place keeper"#

......................................................................................
#color(brown)("Doing the addition")#

#1.5x^3+4.2x^2-37x+0 #
#ul(+4.8x^3+42x^2+0x-89) larr " Add"#
#6.3x^3+46.2x^2-37x-89#