Question

simplify each of the following : (x^2-x+1)^2-(x^2+x+1)^2​

Answer 1

Answer:

-4$x^{3}$ - 4x

Step-by-step explanation:

Step 1 : we will use below formula for solve this question,

$a^{2}$ - $b^{2}$ = (a+b) (a-b)

Step 2 : by using above formula we get,

$( x^{2} - x +1)^{2}$ - $( x^{2} + x +1)^{2}$ = ($x^{2} - x + 1$ + $x^{2} + x + 1$) ($x^{2} - x + 1$ -( $x^{2} + x + 1$) )

we will put value after minus sign in bracket as shown in above.

Step 3 : we will solve small bracket first as shown below

$( x^{2} - x +1)^{2}$ - $( x^{2} + x +1)^{2}$ = ($x^{2} - x + 1$ + $x^{2} + x + 1$) ($x^{2} - x + 1$ - $x^{2} - x - 1$) )

Step 4 :  we will cut same term which has opposite sign in both brackets.

$( x^{2} - x +1)^{2}$ - $( x^{2} + x +1)^{2}$ = ($2x^{2} + 2$ ) ($- 2x$ )

Step 5 : now multiple -2x with the bracket.

$( x^{2} - x +1)^{2}$ - $( x^{2} + x +1)^{2}$ = -4$x^{3}$ - 4x