Algebra mathematical
Introduction :
We are going to see about the topic of algebra mathematics with some examples and their related problems. Algebra plays most important part in mathematics. Some of the algebra concepts are polynomial (addition, subtraction and division), solving equation, and factorization and so on. Algebra also deals with operational rules and it is used to represent the variables in the number form.
Example problems – Algebra mathematics
Example problem 1 – Algebra mathematics Adding the polynomials
(16x2 + 5x - 5) + (8x2 - 9x + 1)
Solution:
The given equation is (16x2 + 5x - 5) + (8x2 - 9x + 1)
The given equation are arranged like term
(16x2 + 5x - 5) + (8x2 - 9x + 1)
16 x2 + 5 x - 5
8 x2 - 9 x + 1
------------------------
24 x2 - 4 x - 4
The correct answer is 24x2 - 4x – 4.
Example problem 2 – Algebra mathematics Using the substitution method to solve the following equations:
2m + 9n = 20 and 4m – 9n = 16.
Solution:
The given equation as follows
2m + 9n = 20 ----- (1)
4m – 9n = 16 ----- (2)
We are going to add the given two equations 2m + 9n = 20 and m – 9b = 16 and remove the n value in the left side because both the value of n is equal and also has different sign.
2m + 9n + 4m – 9n = 20 + 16
2m + 4m + 9n – 9n = 36
Now, the value of n is cancelled,
2m + 4m = 36
6m = 36
m = 6
Substitute the value of m = 6 in the equation 1 or 2 to find the value of n.
2m + 9n = 20
2(6) + 9n = 20
12 + 9n = 20
9n = 20 – 12
9n = 8
n = 8/9
Answer: m = 6 and n = 8/9.
Example problem 3 – Algebra mathematics Find out the value of c from the given equation -g – 34 = 56 + g
Solution:
The given equation is -g – 34 = 56 + g
Process 1: Take the equation -g – 34 = 56 + g
(Arrange to solve the given equation like terms)
Process 2: -g – g = 56 + 34
Add the variable values in left side (both the signs are negative so the variable value will become in negative sign) and add the values in right side
Now, we get
Process 3: -2g = 90
Process 4: -g = 90/2
Process 5: -g = 45
g = -45
Answer: The value of g is -45.
Example problem 4 – Algebra mathematics Find out the value of quotient and remainder for x3 + 2x2 – 4x + 13 and x + 4.
Solution:
The given equation is x3 + 2x2 – 4x + 13
We are going to divide the equation x3 + 2x2 – 4x + 13 by x + 4
Practical problems – Algebra mathematics
Practical problem 1 – Algebra mathematics Subtraction the polynomials
(16x2 + 5x - 5) - (8x2 - 9x + 1)
Answer: 8x2 +14x - 6
Practical problem 2 – Algebra mathematics Find out the value of quotient and remainder for x3 – 9x2 + 4x + 13 and x - 2.
Answer:
Quotient: x2 -7x + 4
Remainder: 21
I like to share this algebra help with you all through my blog.
We are going to see about the topic of algebra mathematics with some examples and their related problems. Algebra plays most important part in mathematics. Some of the algebra concepts are polynomial (addition, subtraction and division), solving equation, and factorization and so on. Algebra also deals with operational rules and it is used to represent the variables in the number form.
Example problems – Algebra mathematics
Example problem 1 – Algebra mathematics Adding the polynomials
(16x2 + 5x - 5) + (8x2 - 9x + 1)
Solution:
The given equation is (16x2 + 5x - 5) + (8x2 - 9x + 1)
The given equation are arranged like term
(16x2 + 5x - 5) + (8x2 - 9x + 1)
16 x2 + 5 x - 5
8 x2 - 9 x + 1
------------------------
24 x2 - 4 x - 4
The correct answer is 24x2 - 4x – 4.
Example problem 2 – Algebra mathematics Using the substitution method to solve the following equations:
2m + 9n = 20 and 4m – 9n = 16.
Solution:
The given equation as follows
2m + 9n = 20 ----- (1)
4m – 9n = 16 ----- (2)
We are going to add the given two equations 2m + 9n = 20 and m – 9b = 16 and remove the n value in the left side because both the value of n is equal and also has different sign.
2m + 9n + 4m – 9n = 20 + 16
2m + 4m + 9n – 9n = 36
Now, the value of n is cancelled,
2m + 4m = 36
6m = 36
m = 6
Substitute the value of m = 6 in the equation 1 or 2 to find the value of n.
2m + 9n = 20
2(6) + 9n = 20
12 + 9n = 20
9n = 20 – 12
9n = 8
n = 8/9
Answer: m = 6 and n = 8/9.
Example problem 3 – Algebra mathematics Find out the value of c from the given equation -g – 34 = 56 + g
Solution:
The given equation is -g – 34 = 56 + g
Process 1: Take the equation -g – 34 = 56 + g
(Arrange to solve the given equation like terms)
Process 2: -g – g = 56 + 34
Add the variable values in left side (both the signs are negative so the variable value will become in negative sign) and add the values in right side
Now, we get
Process 3: -2g = 90
Process 4: -g = 90/2
Process 5: -g = 45
g = -45
Answer: The value of g is -45.
Example problem 4 – Algebra mathematics Find out the value of quotient and remainder for x3 + 2x2 – 4x + 13 and x + 4.
Solution:
The given equation is x3 + 2x2 – 4x + 13
We are going to divide the equation x3 + 2x2 – 4x + 13 by x + 4
Practical problems – Algebra mathematics
Practical problem 1 – Algebra mathematics Subtraction the polynomials
(16x2 + 5x - 5) - (8x2 - 9x + 1)
Answer: 8x2 +14x - 6
Practical problem 2 – Algebra mathematics Find out the value of quotient and remainder for x3 – 9x2 + 4x + 13 and x - 2.
Answer:
Quotient: x2 -7x + 4
Remainder: 21
I like to share this algebra help with you all through my blog.