[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6) = 8x^3+5x^2+2x+3[/tex]
Solution:
Given that we have to perform the indicated operation
Given polynomial is:
[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)[/tex]
Polynomial addition\subtraction is similar to arithmetic addition\subtraction
Add\subtract the terms of coefficients with same variable with same exponent
For example: [tex]x^3 -2x^3 = -x^3[/tex]
To subtract Polynomials, first reverse the sign of each term we are subtracting
Which means, reverse the sign of each term in second bracket
[tex]\rightarrow (7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)\\\\\rightarrow (7x^3 + 11x^2 + 4x + 9)+x^3 - 6x^2 - 2x-6\\\\\text{Remove the parenthesis in first bracket }\\\\\rightarrow 7x^3 + 11x^2 + 4x + 9+x^3 - 6x^2 - 2x-6\\\\\text{Group the similar terms }\\\\\rightarrow 7x^3+x^3+11x^2-6x^2+4x-2x+9-6\\\\\text{Combine the similar terms }\\\\\rightarrow 8x^3+5x^2+2x+3[/tex]
Thus the given operation is performed
