Monomials and binomials are algebraic expressions with one and two terms. Monomials are polynomials with a single term, whereas binomials have two terms joined by an addition or subtraction operation. Monomials and binomials consist of variables, their exponents, coefficients, or constants. A coefficient is a number that appears on the left side of a variable and is connected through multiplication to the variable; for example, in the monomial 7x, “seven” is a coefficient. A constant is a number without an attached variable; for example, in the binomial x + 3, “three” is a constant.
Subtracting Two Monomials
To subtract two monomials, ensure that both the monomials are like or same– which means both the monomials should have the same exponents and variables. For example, 4x^3 and -9x^3 are monomials with like terms since they both have a similar variable and exponent, i.e., x^3. Whereas monomials 5x^2 and -2x are not like terms as their exponents are different, and 8x^2 and -9y^2 are also not like terms because their variables are different. Since only like terms can be subtracted, it is important to carefully compare the monomials for subtracting. Once the variables and exponents are the same, simply subtract the coefficients.
Subtracting One Monomial and One Binomial
To perform the subtraction of monomial and binomial, rearranging these polynomials is important. By rearranging the terms, we can recognize and place the like terms together for subtraction. For example, if we have to subtract the monomial 4x^2 from the binomial 7x^2 + 2x, the terms we will initially write will be 7x^2 + 2x – 4x^2. Here, 7x^2 and -4x^2 are like terms, so we have to write 7x^2 and -4x^2 next to each other to form the expression 7x^2 – 4x^2 + 2x. The next step is to perform the subtraction on the coefficients of the like terms which means subtract 7x^2 – 4x^2 to get 3x^2. Now write the resulting terms together and the solution to the example is 3x^2 + 2x.
Subtracting Two Binomials
Subtracting binomials also requires rearranging like terms and representing binomials in standard form along with applying distributive property to change subtraction to addition. The process of subtracting binomials includes the following steps:
- The first step includes using the distributive property to change subtraction to addition when there are parentheses included. For example, in binomial subtraction, 5x^2 – 5 – (4x^2 – 3), distribute the minus sign before the parentheses to both terms inside it– so, the expression becomes 5x^2 – 5 – 4x^2 +3.
- Rearrange the terms, so that like terms are grouped next to each other– so the above expression becomes 5x^2 – 4x^2 – 5 +3.
- Now solve all like terms by adding or subtracting their coefficients as shown in the problem. To calculate 5x^2 – 4x^2 – 5 +3, solve like terms 5x^2 – 4x^2 to get x^2 and – 5 +3 to get – 2. The final solution of 5x^2 – 5 – (4x^2 – 3) = x^2 – 2.
Learning the concept of polynomials subtraction is essential for studying algebra. Cuemath offers multiple learning resources for kids to understand the concept of monomials and polynomials subtraction with ease. The worksheets and games enable students to understand this concept quickly. To find some interactive resources based on monomials and binomials, visit www.cuemath.com.