Polynomials are used in everyday life, and they find their usage in diverse real-life situations, from shopping to engineering. Learning this important topic helps the students get a broader look at algebra in real life. Learning to perform basic arithmetic operations on polynomials like addition and subtraction requires key skills like identifying the degree of polynomials, their type, and kinds.
In algebra, a polynomial is an expression consisting of two or more variables, coefficients, and arithmetic operators like addition, subtraction, multiplication, and division. The addition or subtraction of polynomials involves simplifying polynomials terms. It simply means adding or subtracting the like terms. Like terms are the terms with the same exponents and variables. Performing the addition or subtraction of polynomials requires the polynomials to be arranged vertically or horizontally. Vertical representation of polynomials is helpful for the addition and subtraction of complex expressions. The horizontal arrangement is helpful for the addition and subtraction of simple expressions.
The addition of polynomials is a simple process. It involves identifying like terms to perform the addition of their coefficients. While adding polynomials, we can use columns to match the correct terms together in a complicated sum. There are majorly two rules to keep in mind while adding polynomials. The first rule is always to pick the like terms together, and the second rule is to keep the signs of all the polynomials the same.
Steps of Adding Polynomials:
- Arrange the polynomial in standard form.
- Identify the like terms in both of the two polynomials.
- Calculate the results with signs remaining the same.
Subtraction of polynomials gets a little tricky, especially when subtracting polynomials with multiple terms. It involves subtracting the coefficient of like terms by keeping them together. While subtracting these terms, it is highly crucial to keep track of the positive and negative signs that correspond to each of these terms. For complex polynomials, it is helpful to keep the correct matching terms together in the columns.
There are two key rules to keep in mind while performing the subtraction of polynomials. First, always take ‘like’ terms together while performing subtraction. And second, change the signs of all the terms of the subtracting polynomial, i.e., change plus sign to minus and minus to plus.
Steps of Subtracting Polynomials:
- Arrange the polynomial in standard form.
- Identify the like terms in both of the polynomials.
- Enclose the subtracting polynomial in parentheses by prefixing a minus sign., Remove the parentheses by changing the sign of each term of the polynomial expression.
- Calculate the result after altering the signs of the subtracting polynomials.
Let’s learn about the two ways to perform polynomial addition and subtraction:
Ways of Adding and Subtracting Polynomials
- Adding and Subtracting Polynomials Horizontally
- Adding and Subtracting Polynomials Vertically
Adding and Subtracting Polynomials Horizontally
Polynomials can be added and subtracted by placing them in a horizontal arrangement. The first and the foremost step is to arrange the polynomials in their standard form and placing the polynomials next to each other horizontally, then Separating the like terms to put them together. Signs of all the polynomials remain the same in addition, whereas for performing subtraction, these signs will change from positive to negative and vice versa.
Adding and Subtracting Polynomials Vertically
Two polynomials can be added and subtracted by putting them in vertical arrangements. This process involves arranging the polynomials in their standard form and placing them in a vertical arrangement, with the like terms placed one above the other. The missing power term can be represented with 0 as the coefficient in the standard form to avoid confusion while arranging terms. Signs of all the polynomials remain the same in addition and change to the opposite in subtraction of polynomials.
Performing arithmetic operations like addition and subtraction of polynomials is a vital skill that every child should acquire to strengthen their algebra skills. Cuemath offers various learning resources like worksheets, puzzles, and games for kids to master the skill of solving polynomial expressions. To learn and practice with these resources.