Adding and Subtracting Polynomials
Description/Explanation/Highlights
Video Description
This video explains how to add and subtract polynomials.
Steps and Key Points to Remember
To add or subtract polynomials, follow these steps:
- To add or subtract polynomials, begin by clearing any grouping symbols (i.e. parenthesis). This may require distributing a number or negative sign to each term in the parenthesis, or if there is only a “+” or nothing in front of the parenthesis, just dropping the parenthesis.
- In the example \((3a^2b+4ab^2+5b^2+2b)+4(2a^2b-3ab^2+2b^2-3b)\), the first set of parenthesis around the 4-term polynomial would be dropped but the 4 in front of the second 4-term polynomial must be distributed to all four terms in the parenthesis. After distributing and rewriting the result will be: \(3a^2b+4ab^2+5b^2+2b+8a^2b-12ab^2+8b^2-12b\)
- After eliminating grouping symbols, combine like terms. Remember: terms are only “like” if the contain exactly the same variables with exactly the same exponents. For example, \(3a^2b\) and \(8a^2b\) are like terms and can be combined by adding the coefficients together. The resulting term will be \(11a^2b\).
- After combining like terms in the previous polynomial addition example, the result will be: \(11a^2b-8ab^2+13b^2-10b\). Notice the result is always written in alphabetical order and from largest to smallest exponent.
- Subtraction is done the same as addition except care must be taken to distribute the “-” sign to all terms in the polynomial being subtracted.
- In the subtraction example, \((4x^3y^2-3x^2y+2xy^2+3y)-(2x^3y^2+2x^2y-y)\), the first set of parenthesis is dropped and the “-” is distributed to all the terms in the second polynomial. The result will be: \(4x^3y^2-3x^2y+2xy^2+3y-2x^3y^2-2x^2y+y\)
- To complete the problem, combine like terms. The final answer will be: \(2x^3y^2-5x^2y+2xy^2+4y\)
- If there is a number as well as a subtraction sign in front of the polynomial to be subtracted, the number as well as the sign must be distributed as in the example: \(2(5x^2y-2xy^2+3x-y)-4(x^2y-2xy^2-2x+5y)\)
- In the above example, the 2 must be distributed to all the terms in the first polynomial and the -4 must be distributed to the second. The result will be: \(10x^2y-4xy^2+6x-2y-4x^2y+8xy^2+8x-20y\) before combining like terms and the final answer will be: \(6x^2y+4xy^2+14x-22y\)
Here are some key points to keep in mind when adding and subtracting polynomials.
- Always start by getting rid of parenthesis by either dropping them if there is nothing in front of the parenthesis or distributing anything in front of the parenthesis, including a negative sign, to all terms in the parenthesis.
- After parenthesis are eliminated, combine like terms.
- Like terms are those whose variables are exactly alike and exponents are exactly the same.
- Combine by combining the coefficients and keeping the variables and exponents the same.
- Subtraction is done the same way as addition but care must be taken to distribute the negative sign to all terms in the second polynomial.
Video Highlights
- 00:00 Introduction
- 00:15 Steps for adding and subtracting a polynomial
- 01:09 \((3a^2b+4ab^2+5b^2+2b)+4(2a^2b-3ab^2+2b^2-3b)\) polynomial addition example
- 04:35 \((4x^3y^2-3x^2y+2xy^2+3y)-(2x^3y^2+2x^2y-y)\) subtraction example
- 07:00 \(2(5x^2y-2xy^2+3x-y)-4(x^2y-2xy^2-2x+5y)\) subtraction example with distribution
- 09:00 Conclusion
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