Simple Algebra Introduction:
A Simple Algebra follows the rules as in arithmetic. Algebra includes vectors, real and complex numbers etc. Comparing Arithmetic with Algebra we will look something like this: in Arithmetic: 9 + 2 = 9 + 2 in Algebra: 3x + 4y = 5y. Algebra performs the operation with variables and numbers are: addition, subtraction, multiplication, and division.
Algebra is widely used in day to day activities watch out for my forthcoming posts on free college algebra solver and algebra expression solver. I am sure they will be helpful.
Simple Algebra Practice Formulas:
Some Important Simple Algebra Practice Formulas and Definitions:
Commutative property of addition: a + b = b + a
Associative Property of Multiplication: (a + b) + c = a + (b + c)
Commutative property of multiplication: a × b = b × a
Identity property of multiplication: a × 1 = a
Inverse property of multiplication: a × 1/a = 1
Midpoint formula: [(x2 + x1) ÷ 2], [(y2 + y1) ÷ 2]
Simple Algebra Practice Problems:
Ex 1 : Simplify 13x + 7y − 2x + 6a
Sol : 13x + 7y − 2x + 6a
The only like terms in this expression are 13x and -2x. We cannot do anything with the 7y or 6a.
So we group mutually the terms we can subtract, and just leave the rest:
(13x − 2x) + 6a + 7y
= 6a + 11x + 7y
Ex 2: Multiply (2x + 3)(x2 − x − 5)
Sol: We take the 2 terms of the first bracket and multiply both of them by the second bracket.
(2x + 3)(x2− x − 5)
= (2x)(x2 − x − 5) + (3)(x2 − x − 5)
= (2x3 − 2x2 − 10x) + (3x2 − 3x − 15)
= 2x3 + x2 − 13x − 15
This time we could collect together some like terms. There was:
-2x2 + 3x2 = x2
and
-10x − 3x = -13x
Ex 3 : Multiply (x + 3)(x2 − x − 5)
Sol : We take the 2 terms of the first bracket and multiply both of them by the second bracket.
(x + 3)(x2− x − 5)
= (x)(x2 − x − 5) + (3)(x2 − x − 5)
= (x3 − x2 − 5x) + (3x2 − 3x − 15)
= x3 + 2x2 − 8x − 15
Ex 4: 26 + j = 13 + 13 + j
Sol : Combine like terms: 13 + 13 = 26
26 + j = 26 + j
Add '-26' to each side of the equation.
26 + -26 + j = 26 + -26 + j
Combine like terms: 26 + -26 = 0
0 + j = 26 + -26 + j
j = 26 + -26 + j
Combine like terms: 26 + -26 = 0
j = 0 + j
j = j
Add '-1j' to each side of the equation.
j + -1j = j + -1j
Combine like terms: j + -1j = 0
0 = j + -1j
Combine like terms: j + -1j = 0
0 = 0
This equation is an identity, all real numbers are solutions.
A Simple Algebra follows the rules as in arithmetic. Algebra includes vectors, real and complex numbers etc. Comparing Arithmetic with Algebra we will look something like this: in Arithmetic: 9 + 2 = 9 + 2 in Algebra: 3x + 4y = 5y. Algebra performs the operation with variables and numbers are: addition, subtraction, multiplication, and division.
Algebra is widely used in day to day activities watch out for my forthcoming posts on free college algebra solver and algebra expression solver. I am sure they will be helpful.
Simple Algebra Practice Formulas:
Some Important Simple Algebra Practice Formulas and Definitions:
Commutative property of addition: a + b = b + a
Associative Property of Multiplication: (a + b) + c = a + (b + c)
Commutative property of multiplication: a × b = b × a
Identity property of multiplication: a × 1 = a
Inverse property of multiplication: a × 1/a = 1
Midpoint formula: [(x2 + x1) ÷ 2], [(y2 + y1) ÷ 2]
Simple Algebra Practice Problems:
Ex 1 : Simplify 13x + 7y − 2x + 6a
Sol : 13x + 7y − 2x + 6a
The only like terms in this expression are 13x and -2x. We cannot do anything with the 7y or 6a.
So we group mutually the terms we can subtract, and just leave the rest:
(13x − 2x) + 6a + 7y
= 6a + 11x + 7y
Ex 2: Multiply (2x + 3)(x2 − x − 5)
Sol: We take the 2 terms of the first bracket and multiply both of them by the second bracket.
(2x + 3)(x2− x − 5)
= (2x)(x2 − x − 5) + (3)(x2 − x − 5)
= (2x3 − 2x2 − 10x) + (3x2 − 3x − 15)
= 2x3 + x2 − 13x − 15
This time we could collect together some like terms. There was:
-2x2 + 3x2 = x2
and
-10x − 3x = -13x
Ex 3 : Multiply (x + 3)(x2 − x − 5)
Sol : We take the 2 terms of the first bracket and multiply both of them by the second bracket.
(x + 3)(x2− x − 5)
= (x)(x2 − x − 5) + (3)(x2 − x − 5)
= (x3 − x2 − 5x) + (3x2 − 3x − 15)
= x3 + 2x2 − 8x − 15
Ex 4: 26 + j = 13 + 13 + j
Sol : Combine like terms: 13 + 13 = 26
26 + j = 26 + j
Add '-26' to each side of the equation.
26 + -26 + j = 26 + -26 + j
Combine like terms: 26 + -26 = 0
0 + j = 26 + -26 + j
j = 26 + -26 + j
Combine like terms: 26 + -26 = 0
j = 0 + j
j = j
Add '-1j' to each side of the equation.
j + -1j = j + -1j
Combine like terms: j + -1j = 0
0 = j + -1j
Combine like terms: j + -1j = 0
0 = 0
This equation is an identity, all real numbers are solutions.
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