How to subtract signed numbers?   Example: 1. {-(-27n)+(36)} -n^3 {2n-4n^3(59)+(-73)}I dont understand how to compute it and what will I do to the exponent.

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lemjay | High School Teacher | (Level 3) Senior Educator

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{-(-27n) + (36)} - n^3{2n -4n^3(59) + (-73)}

Start by simplying the terms inside the bracket { }.

>> for { -(-27n) + (36) }  = 27n + 36

Note that if a number is preceded by two consecutive negatives, the resulting sign of the number is positive. This follows the rule for multiplication of LIKE SIGNs.

>> for {2n - 4n^3(59) + (-73) } = 2n - 4n^3(59) - 73

                                                = 2n - 236n^3 - 73 

The resulting sign of +(-73) is negative. This is under the rule of multiplication of UNLIKE Signs.

We would then have,

 27n + 36 - n^3(2n - 236n^3 - 73).

Next, simplify -n^3 (2n - 236n^3 - 73) using distributive property.

>> -n^3 (2n - 236n^3 - 73) = -2n^4 + 236n^6 + 73n^3.

To multiply same variables with exponents, add the exponents.

We would then have,

27n + 36 - 2n^4 + 236n^6 + 73n^3

= 236n^6 - 2n^4 + 73n^3 + 27n + 36 

Answer: 236n^6 - 2n^4 + 73n^3 + 27n + 36 

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