Monomials are integer algebraic expressions that have only products between the coefficients and the literal part. Note some monomials:
In a monomium we can observe a literal part and a numerical part (coefficient). Look:
5x³
Coefficient: 5
Literal part: x³
17axb
Coefficient: 17
Literal part: axb
Addition and subtraction of monomials
When adding and subtracting monomials we must take into account the similar literal parts, adding or subtracting the coefficients and preserving the literal part. See examples:
17x³ + 20x³ = (17 + 20)x³ = 37x³
2ax² + 10b – 6ax² – 8b = (2 – 6)ax² + (10 – 8)b = –4ax² + 2b
–4xy + 6xy – 5xy = (–4 + 6 –5)xy = – 3xy
5b³ + 7c³ + 6b³ – 2c³ = (5 + 6)b³ + (7 – 2)c³ = 11b³ + 5c³
Multiplication of monomials
In monomial multiplication we must multiply coefficient by coefficient and literal part by literal part. When multiplying equal literal parts, apply the multiplication of powers of equal bases: add the exponents and repeat the base.
2x * 3x = (3 * 2) * (x * x) = 6 * x² = 6x²
4x * 6z = (4 * 6) * (x * z) = 24 * xz = 24xz
5b² * 10b² * c³ = (5 * 10) * (b² * b² * c³) = 50 * b4c³ = 50b4c³
4a²x³ * (–5ax²) = [4*(–5)] * (a²x³ * ax²) = –20 * a³x5 = -20a³x5
monomial division
When dividing monomials we must divide coefficient by coefficient and literal part by literal part. When dividing literal equal parts, apply the division of powers of equal bases: subtract the exponents and repeat the base.
16x5: 4x² = 4x³ → (16:4) and (x5: x²)
20a²x³: (–5ax²) = –4ax → [20: (–5)] and (a²x³: ax²)
81x: 9x = 9
144x³b²: 2xb = 72x²b
by Mark Noah
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/calculo-algebrico-envolvendo-monomios.htm