Question

Find the value of $a + {a^2} - {a^3} + {a^4} - {a^5}$if $a = - \,2$.
A. $ - 22$
B. $ - 18$
C. $32$
D. $58$

Answer 1

Hint: In this question, we will put the value of a in the above information. Further we will solve the equation to get the desired result.


Complete step by step solution:
 $a + {a^2} - {a^3} + {a^4} - {a^5}$…(i)
$a = - 2\left( {given} \right)$
Put the value of $a = - 2$ in equation (i)
$ = \left( { - 2} \right) + {\left( { - 2} \right)^2} - {\left( { - 2} \right)^3} + {\left( { - 2} \right)^4} - {\left( { - 2} \right)^5}$
$ = \left( { - 2} \right) + \left( { - 2x - 2} \right) - \left( { - 2x - 2x - 2} \right) + \left( { - 2x - 2x - 2x - 2} \right) - \left( { - 2x - 2x - 2x - 2x - 2} \right)$
$ = - 2 + 4 - \left( { - 8} \right) + 16 - \left( { - 32} \right)$ $\left[ { - \left( { - 1} \right)\, = + 1\,\,because\,of\,\left( - \right)\,and\,\left( - \right)\,both\,\,multiply\,\,then\,\,we\,\,have\, + 1} \right]$
$ = - 2 + 4 + 8 + 16 + 32$
$ = - 2 + 12 + 16 + 32$
$ = - 2 + 28 + 32$
$ = - 2 + 60$
$ = 58$ ans.


Note: Students must keep in mind that odd powers of negative numbers will give us negative answers and even power of negative numbers will give us positive answers.