In situations involving algebraic calculations, it is extremely important to apply rules in the operations between monomials. The situations presented here will address the addition, subtraction, and multiplication of polynomials.
Addition and Subtraction
Consider the polynomials –2x² + 5x – 2 and –3x³ + 2x – 1. Let's add and subtract between them.
Addition
(–2x² + 5x – 2) + (–3x³ + 2x – 1) → eliminate the parentheses by performing the sign match
–2x² + 5x – 2 – 3x³ + 2x – 1 → reduce similar terms
–2x² + 7x – 3x³ – 3 → sort in descending order according to power
–3x³ – 2x² + 7x – 3
Subtraction
(–2x² + 5x – 2) – (–3x³ + 2x – 1) → eliminate the parentheses by performing the signal match
–2x² + 5x – 2 + 3x³ – 2x + 1 → reduce similar terms
–2x² + 3x – 1 + 3x³ → sort in descending order according to power
3x³ - 2x² + 3x - 1
Multiplication of polynomial by monomium
For a better understanding, look at the example:
(3x2) * (5x3 + 8x2 – x) → apply the distributive property of multiplication
15x5 + 24x4 – 3x3
Polynomial by Polynomial Multiplication
To carry out the multiplication of polynomial by polynomial we must also use the distributive property. See the example:
(x – 1) * (x2 + 2x - 6)
x2 * (x – 1) + 2x * (x – 1) – 6 * (x – 1)
(x³ - x²) + (2x² - 2x) - (6x - 6)
x³ – x² + 2x² – 2x – 6x + 6 → reducing similar terms.
x³ + x² - 8x + 6
Therefore, in the multiplications between monomials and polynomials we apply the distributive property of multiplication.
by Mark Noah
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/adicao-subtracao-e-multiplicacao-de-polinomios.htm
