Mathematical algebra
Introduction :
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary algebra.(Source – Wikipedia)
Mathematical Algebra in Algebraic Expressions:
The followings are some of the examples for algebraic expressions in algebra.
Mathematical Expressions:
The given expressions are 20x + 7y + 3x + 4a
From them the like terms are 20x and 3x. Then we cannot do anything in 7y or 4a.
By adding the group terms.
= (20x +3x) + 4a + 7y
= 4a + 23x + 7y.
The given expressions are 30x - 9y - 3x - 7a
From them the like terms are 30x and 3x. Then we cannot do anything in 9y or 7a.
By subtracting the group terms.
= (30x -3x) - 7a - 9y
= 7a - 27x - 9y
Mathematical Algebra in Polynomials:
The followings are some of the Polynomials Examples in algebra.
Mathematical Polynomials:
By adding the two polynomials.
= (9x4 – 5x2 + 3x + 4) + (2x3 – 6x2 + 4x – 1)
= 9x4 + 2x3 – 5x2 – 6x2 + 3x + 4x + 4 – 1
Equating the two polynomial.
= 9x4 + 2x3 – (5+6) x2 + (3+4) x + 3
= 9x4 + 2x3 – 11x2 + 7x + 3.
We can multiplying the two given polynomials.
= (9x3 – 3x2 – 4) (2x2 + 3x – 1)
= 9x3 (2x2 + 3x – 1) + (–3x2) (2x2 + 3x – 1) + (–4) (2x2 + 3x – 1)
= (18x5 + 27x4 – 9x3) + (–6x4 – 9x3 + 3x2) + (–8x2 – 12x + 4)
We can equating the two given polynomials.
= 18x5 + 27x4 – 9x3 – 6x4 – 9x3 + 3x2 – 8x2 – 12x + 4
= 18x5 + (27x4 – 6x4) + (–9x3 – 9x3) + (3x2 – 8x2) + (–12x) + 4
= 18x5 + 21x4 – 18x3 – 5x2 – 12x + 4.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary algebra.(Source – Wikipedia)
Mathematical Algebra in Algebraic Expressions:
The followings are some of the examples for algebraic expressions in algebra.
Mathematical Expressions:
- Find the algebraic expressions of addition: 20x + 7y + 3x + 4a.
The given expressions are 20x + 7y + 3x + 4a
From them the like terms are 20x and 3x. Then we cannot do anything in 7y or 4a.
By adding the group terms.
= (20x +3x) + 4a + 7y
= 4a + 23x + 7y.
- Find the algebraic expressions of subtraction: 30x - 9y - 3x - 7a.
The given expressions are 30x - 9y - 3x - 7a
From them the like terms are 30x and 3x. Then we cannot do anything in 9y or 7a.
By subtracting the group terms.
= (30x -3x) - 7a - 9y
= 7a - 27x - 9y
Mathematical Algebra in Polynomials:
The followings are some of the Polynomials Examples in algebra.
Mathematical Polynomials:
- Find the sum of 9x4 – 5x2 + 3x + 4 and 4x + 2x3 – 6x2 – 1.
By adding the two polynomials.
= (9x4 – 5x2 + 3x + 4) + (2x3 – 6x2 + 4x – 1)
= 9x4 + 2x3 – 5x2 – 6x2 + 3x + 4x + 4 – 1
Equating the two polynomial.
= 9x4 + 2x3 – (5+6) x2 + (3+4) x + 3
= 9x4 + 2x3 – 11x2 + 7x + 3.
- Find the product of 9x3 – 3x2 – 4 and 2x2 + 3x – 1.
We can multiplying the two given polynomials.
= (9x3 – 3x2 – 4) (2x2 + 3x – 1)
= 9x3 (2x2 + 3x – 1) + (–3x2) (2x2 + 3x – 1) + (–4) (2x2 + 3x – 1)
= (18x5 + 27x4 – 9x3) + (–6x4 – 9x3 + 3x2) + (–8x2 – 12x + 4)
We can equating the two given polynomials.
= 18x5 + 27x4 – 9x3 – 6x4 – 9x3 + 3x2 – 8x2 – 12x + 4
= 18x5 + (27x4 – 6x4) + (–9x3 – 9x3) + (3x2 – 8x2) + (–12x) + 4
= 18x5 + 21x4 – 18x3 – 5x2 – 12x + 4.