Adding polynomials
Adding Polynomials explains how to combine two polynomials by removing parentheses and combining like terms — terms that share exactly the same variable factors and exponents. This operation is taught in Yoshiwara Elementary Algebra Chapter 7: Polynomials and is an essential Grade 6 algebra skill for simplifying expressions and solving equations. When adding, only coefficients change; exponents on variables remain unchanged.
Key Concepts
Property To add two polynomials we remove parentheses and combine like terms. Like terms are any terms that are exactly alike in their variable factors. The exponents on the variable factors must also match. To add like terms, we add their numerical coefficients.
Examples To simplify $3x^2 + 5x^2$, we add the coefficients to get $(3+5)x^2 = 8x^2$. The expression $3x^2 + 5x^3$ cannot be simplified.
Add $(4a^3 2a^2 3a + 1) + (2a^3 + 4a 5)$. This simplifies to $6a^3 2a^2 + a 4$.
Common Questions
How do you add two polynomials?
Remove the parentheses and then identify and combine like terms — terms with the same variable and exponent. Add their coefficients while keeping the variable part unchanged.
What are like terms in a polynomial?
Like terms have the exact same variables raised to the same powers. For example, 3x² and -7x² are like terms, but 3x² and 3x are not.
Can you add terms with different exponents?
No. Terms with different exponents cannot be combined. For example, 4x² + 3x cannot be simplified further because x² and x are not like terms.
Where is adding polynomials covered in Yoshiwara Elementary Algebra?
Adding polynomials is taught in Chapter 7: Polynomials of Yoshiwara Elementary Algebra.
What is the difference between adding and multiplying polynomials?
When adding, you only combine like terms. When multiplying, you distribute each term and may create new terms that then need to be combined.