Question

Simplify the given equation $(a^3-2a^2+4a-5)$ - $(-a^3-8a+2a^2+5)$
A.$2a^3 + 7a^2 + 6a - 10$
B.$2a^3 + 7a^2 + 12a - 10$
C.$2a^3 - 4a^2 + 12a - 10$
D.$2a^3 - 4a^2 + 6a - 10$

Answer 1

Hint: To Simplify first open the bracket with a negative sign as given outside in the second bracket term. Then solve the like terms.

Complete step-by-step answer:
Step 1: Open the brackets
${a^3} - 2{a^2} + 4a - 5 - ( - {a^3}) - ( - 8a) - ( + 2{a^2}) - ( + 5)$
$ = {a^3} - 2{a^2} + 4a - 5 + {a^3} + 8a - 2{a^2} - 5$
Step 2: Write the like terms together
$ \Rightarrow ({a^3} + {a^3}) + ( - 2{a^2} - 2{a^2}) + ( + 4a + 8a) + ( - 5 - 5)$
Step 3: Solve the like terms
$ \Rightarrow 2{a^3} - 4{a^2} + 12a - 10$
Now look for the options.
Hence, Option(c) is correct.
There are some rules while solving the signs -
In Multiplication:
If two numbers are of different sign $( + ) \times ( - ) = ( - )$
If two numbers are of different sign $( - ) \times ( + ) = ( - )$
If two numbers are of same sign $( - ) \times ( - ) = ( + )$
If two numbers are of same sign $( + ) \times ( + ) = ( + )$

In Addition:
If two numbers have the same sign i.e., positive (+) positive (+) or negative (-) negative (-), then there should be a simple addition of numbers and the sign is the sign of a bigger number.
If two numbers have different signs i.e., positive(+) negative(-) or negative(-) positive(+), then there should be a simple subtraction of two numbers from bigger - smaller such that the result has a sign of bigger number.

Note: While solving always remember and look for the sign. Most of the students made mistakes while solving or opening the bracket. Also, look for the sign of like terms that they are adding or subtracting, for this additional information is written below.