Answer the following questions on like terms and their use in polynomial addition:
MATHEMATICS · Multi-part · AoPS · Mathematics · x Marks the Spot · x Marks the Spot
Problem
Answer the following questions on like terms and their use in polynomial addition:
(i) Define like terms in the context of polynomials.
(ii) State, with reason, whether the terms 3x2y and −7xy2 are like terms.
(iii) When two polynomials are added, why must only the coefficients of like terms be combined? Give a brief explanation in two to three sentences.
(iv) Write two polynomials in one variable that are not arranged in descending powers of the variable. Rearrange each polynomial in standard form and then add them term-wise.