Answer: Adding and subtracting polynomials are both arithmetic operations used in algebra. The main difference between the two operations is the sign of the terms being combined.
Adding polynomials involves combining like terms by adding their coefficients. When adding polynomials, the terms being added have the same sign. For example, when adding the polynomials x^2 + 2x + 1 and 3x^2 + 4x + 2, we combine the like terms (x^2 terms, x terms, and constant terms) by adding their coefficients:
(x^2 + 2x + 1) + (3x^2 + 4x + 2) = 4x^2 + 6x + 3
Subtracting polynomials involves subtracting one polynomial from another by changing the sign of each term in the polynomial being subtracted and then adding the resulting polynomials. When subtracting polynomials, the terms being subtracted have opposite signs. For example, when subtracting the polynomial 3x^2 + 4x + 2 from the polynomial x^2 + 2x + 1, we first change the sign of each term in the polynomial being subtracted:
(x^2 + 2x + 1) - (3x^2 + 4x + 2) = x^2 + 2x + 1 - 3x^2 - 4x - 2
Then, we combine the like terms by adding their coefficients:
x^2 - x - 1
In summary, the main difference between adding and subtracting polynomials is that adding involves combining like terms with the same sign, while subtracting involves changing the sign of one polynomial and then adding the resulting polynomials.
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