The algebraic expressions present in mathematics are called polynomials. A polynomial is any expression that has an algebraic addition and/or subtraction of monomials.
In order to perform algebraic calculations in this structure, we must first reduce the polynomial expression, that is, gather similar terms. Before we learn how to do this, let's look back at the structure of a monomium.
Every monomium has a numerical part and a literal part. |
Now that we've remembered the structure of a monomial and since we already know that the polynomial is composed of monomials, let's see what the “reduction of a polynomial” is.
To reduce polynomials we must first join the terms of the same literal part, then we perform the operation between the coefficients. Note the examples below:
Example 1:
12x2– 10x+ 4– 6x2+ 14x - x = Identify the distinct literal parts.
= 12x2– 6x2– 10x + 14x – x+ 4 = Rearrange the terms and place those of the same literal part next to each other.
= 6x2+ 4x - x+ 4 = Perform the reduction of similar terms. To do this, carry out the operations with the coefficients of the same literal part.
= 6x2+ 3x+ 4
Example 2:
5th+ 4b– 6– 12b+ 2nd– 3 =Identify the distinct literal parts.
= 5th + 2nd – 12b+ 4b– 6 – 3 = Rearrange the terms and place those of the same literal part next. Then carry out the reduction of similar terms.
= 7The– 8b– 9
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Example 3
6ab+ 4xy+ 4th+ x– 5ab– 4xy– 2x = Identify the distinct literal parts.
= 6ab - 5ab+ 4xy - 4xy+ x – 2x+ 4th = Rearrange the terms and place those of the same literal part next to each other.
= ab+ 0– x+ 4th = Carry out the operation with the coefficients of the same literal part, that is, reduction of similar terms.
= ab– x+ 4th
You can see that in the examples above we only work with the addition and subtraction operators. We will now see how to perform the reduction calculations of a polynomial algebraic expression, when we have the operations of multiplication and division. Check out the following examples:
Example 1
(2x. 4yx) + 5xy - x + (25x: 5) = Solve parentheses operations.
= 8yx2 + 5xy - x + 5x = Identify distinct literal parts, rearrange and place terms from the same literal part next to each other.
= 8yx2 + 5xy + 4x
Example 2
(15xy: 3) + (2. 4x) - 5xy - 8x =Solve parentheses operations.
= 5xy + 8x – 5xy – 8x = Identify distinct literal parts, rearrange and place terms from the same literal part next to each other.
= 5xy - 5xy + 8x - 8x =
= 0
Now that you understand what the reduction of a polynomial is, keep practicing. Good studies!
By Naysa Oliveira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
OLIVEIRA, Naysa Crystine Nogueira. "Polynomial reduction"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/reducao-polinomio.htm. Accessed on June 28, 2021.
