Algebraic Calculus Involving Monomials

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 = 50b4
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

Israeli company offers Coca-Cola vouchers as compensation to thousands of customers

Israeli company offers Coca-Cola vouchers as compensation to thousands of customers

Israel's dominant soft drink production company, which distributes the brand Coke for the whole c...

read more
You can find the answers to the word search below using the hints.

You can find the answers to the word search below using the hints.

EntertainmentLook among the scrambled letters for the names of some elements that are found in pa...

read more

WhatsApp update has a secret menu; know how to find it

So that an application does not become obsolete in time changes, it needs to be always updating. ...

read more