Question

Perform the indicated operation.

Answer 1

$(7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6) = 8x^3+5x^2+2x+3$

Solution:

Given that we have to perform the indicated operation

Given polynomial is:

$(7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)$

Polynomial addition\subtraction is similar to arithmetic addition\subtraction

Add\subtract the terms of coefficients with same variable with same exponent

For example: $x^3 -2x^3 = -x^3$

To subtract Polynomials, first reverse the sign of each term we are subtracting

Which means, reverse the sign of each term in second bracket

$\rightarrow (7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)\\\\\rightarrow (7x^3 + 11x^2 + 4x + 9)+x^3 - 6x^2 - 2x-6\\\\\text{Remove the parenthesis in first bracket }\\\\\rightarrow 7x^3 + 11x^2 + 4x + 9+x^3 - 6x^2 - 2x-6\\\\\text{Group the similar terms }\\\\\rightarrow 7x^3+x^3+11x^2-6x^2+4x-2x+9-6\\\\\text{Combine the similar terms }\\\\\rightarrow 8x^3+5x^2+2x+3$

Thus the given operation is performed