Online algebra teacher
Introduction :
In online algebra teacher, the 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.Let us see how the online algebra teaches.
(Source – Wikipedia)
Online Teacher in Algebra Contents:
The followings are some of the contents to teach algebra in online.
The followings are some of the examples for online algebra teacher.
Solution:
1013 = (1000 + 1)3
Use the identity (a + b)3 = a3 + b3 +3ab (a + b)
= 1003 + 13 + 3 * 100 * 1 (100 + 1)
= 1000000 + 1 + 300 (100 + 1)
= 1000000 + 1 + 30000 + 300 (by simplifying)
= 1030301
Comparing the given expression (2a + 3b + 4c)2 with (a + b + c)2, we have
From the given expression.
a = 2a
b = 3b
c =4c
(2a + 3b + 4c)2 = (2a)2 + (3b)2 + (4c)2 + 2 (2a) (3b) + 2 (3b) (4c) + 2 (4c) (2a)
= 4a2 + 9b2 + 16c2 + 12ab + 24bc + 16ca
Solution:
`(x^2+x-1)/(x^2+ 8x+15) ` = 1 + `(8x+15)/(x^2+8x+15)` ----> (1)
Let` (8x+15)/(x^2+8x+15)` = ` A/(x + 5 )` + `B/(x + 3)`
8x + 15 = A(x + 5) + B(x + 3)
By putting x = -3,
2A = -24+15
2A = -9
A = `-9/2`
By putting x = -5,
B = -40 + 15
B = -25
B = 25
Therefore, `(x^2+x-1)/(x^2+8x+15) ` = `(-9/2)/(x + 5)` + `(25/3)/(x + 3)`
=> `(x^2+x-1)/(x^2+8x+15)` = `(1-9/2)/(x+ 5)` +`25/(x + 3)` is the solution for the given partial fraction.
Divide: 24x5y2z – 12x2y2z + 36x2yz by -6xyz.
Solution:
(24x5y2z – 12x2y2z + 6x2yz) ÷ -6xyz.
= `(24x^5y^2z)/-6xyz` - `(12x^2y^2z)/-6xyz` + `(6x^2yz)/-6xyz`
= -4x5-1 y2-1 + 2x2-1 y2-1 z2-2 – x2-1 y1-1 z1-1 (by dividing)
= -4x4 y + 2xy – x
In online algebra teacher, the 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.Let us see how the online algebra teaches.
(Source – Wikipedia)
Online Teacher in Algebra Contents:
The followings are some of the contents to teach algebra in online.
- Algebraic Identities
- Partial Fraction
- Algebraic Expression
The followings are some of the examples for online algebra teacher.
- Algebraic Identities:
Solution:
1013 = (1000 + 1)3
Use the identity (a + b)3 = a3 + b3 +3ab (a + b)
= 1003 + 13 + 3 * 100 * 1 (100 + 1)
= 1000000 + 1 + 300 (100 + 1)
= 1000000 + 1 + 30000 + 300 (by simplifying)
= 1030301
- Expand (2a + 3b + 4c)2
Comparing the given expression (2a + 3b + 4c)2 with (a + b + c)2, we have
From the given expression.
a = 2a
b = 3b
c =4c
(2a + 3b + 4c)2 = (2a)2 + (3b)2 + (4c)2 + 2 (2a) (3b) + 2 (3b) (4c) + 2 (4c) (2a)
= 4a2 + 9b2 + 16c2 + 12ab + 24bc + 16ca
- Partial Fraction:
Solution:
`(x^2+x-1)/(x^2+ 8x+15) ` = 1 + `(8x+15)/(x^2+8x+15)` ----> (1)
Let` (8x+15)/(x^2+8x+15)` = ` A/(x + 5 )` + `B/(x + 3)`
8x + 15 = A(x + 5) + B(x + 3)
By putting x = -3,
2A = -24+15
2A = -9
A = `-9/2`
By putting x = -5,
B = -40 + 15
B = -25
B = 25
Therefore, `(x^2+x-1)/(x^2+8x+15) ` = `(-9/2)/(x + 5)` + `(25/3)/(x + 3)`
=> `(x^2+x-1)/(x^2+8x+15)` = `(1-9/2)/(x+ 5)` +`25/(x + 3)` is the solution for the given partial fraction.
Divide: 24x5y2z – 12x2y2z + 36x2yz by -6xyz.
Solution:
(24x5y2z – 12x2y2z + 6x2yz) ÷ -6xyz.
= `(24x^5y^2z)/-6xyz` - `(12x^2y^2z)/-6xyz` + `(6x^2yz)/-6xyz`
= -4x5-1 y2-1 + 2x2-1 y2-1 z2-2 – x2-1 y1-1 z1-1 (by dividing)
= -4x4 y + 2xy – x