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Algebra for Beginners | Basics of Algebra
Geek's Lesson UCKXx22vOENUyHrVAADq7Z_g
Topics
Summary Copy Link
Simplifying Fractions in Algebra
Sure, I’d be happy to help! Here’s a summary of the “Introduction to Algebra” chapter,
including examples, quotes, and visuals.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the rules for
manipulating those symbols. It’s a powerful tool that allows us to solve complex problems
by representing unknowns with symbols and then manipulating those symbols according
to certain rules.
As mathematician Muhammad ibn Musa al-Khwarizmi, known as the father of algebra,
once said: “The science of Algebra is so useful in various branches of science and art that
no one can ignore it without being deprived of the advantages and benefits deriving
therefrom.”
Basic Algebraic Expressions
At the heart of algebra are algebraic expressions. These are mathematical phrases that
can contain numbers, variables (such as x or y), and operators (such as addition,
subtraction, multiplication, and division).
, For example, the following are all algebraic expressions:
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3x + 2
4y - 7
(x + 3)(y - 2)
The last expression, (x + 3)(y - 2), is an example of a product of two binomials. A binomial
is a polynomial with exactly two terms, such as x + 3 or y - 2.
To evaluate a binomial product, you can use an area model, as shown in the following
video:
<iframe width="560" height="315" src="https://www.youtube-
nocookie.com/embed/lKDqzrrO82Y" title="YouTube video player" frameborder="0"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-
picture" allowfullscreen></iframe>
In this example, we want to find the product of (x + 3) and (y - 2). To do this, we first draw
a rectangle and label the sides with the binomials:
Next, we fill in the rectangle with the appropriate terms:
Finally, we read off the product:
xy - 2x + 3y - 6
This is an example of the FOIL method for binomial multiplication, where FOIL stands for
First, Outer, Inner, Last.
Equations and Inequalities
Algebra is also used to solve equations and inequalities. An equation is a statement that
two expressions are equal, while an inequality is a statement that one expression is
greater than or less than another expression.
For example, the following are all equations:
2x + 3 = 7
x^2 - 4 = 0
(x + 2)(x - 3) = 0
To solve an equation, we need to find the value(s) of the variable(s) that make the
equation true.
Algebra for Beginners | Basics of Algebra
Geek's Lesson UCKXx22vOENUyHrVAADq7Z_g
Topics
Summary Copy Link
Simplifying Fractions in Algebra
Sure, I’d be happy to help! Here’s a summary of the “Introduction to Algebra” chapter,
including examples, quotes, and visuals.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the rules for
manipulating those symbols. It’s a powerful tool that allows us to solve complex problems
by representing unknowns with symbols and then manipulating those symbols according
to certain rules.
As mathematician Muhammad ibn Musa al-Khwarizmi, known as the father of algebra,
once said: “The science of Algebra is so useful in various branches of science and art that
no one can ignore it without being deprived of the advantages and benefits deriving
therefrom.”
Basic Algebraic Expressions
At the heart of algebra are algebraic expressions. These are mathematical phrases that
can contain numbers, variables (such as x or y), and operators (such as addition,
subtraction, multiplication, and division).
, For example, the following are all algebraic expressions:
SolidPoint
3x + 2
4y - 7
(x + 3)(y - 2)
The last expression, (x + 3)(y - 2), is an example of a product of two binomials. A binomial
is a polynomial with exactly two terms, such as x + 3 or y - 2.
To evaluate a binomial product, you can use an area model, as shown in the following
video:
<iframe width="560" height="315" src="https://www.youtube-
nocookie.com/embed/lKDqzrrO82Y" title="YouTube video player" frameborder="0"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-
picture" allowfullscreen></iframe>
In this example, we want to find the product of (x + 3) and (y - 2). To do this, we first draw
a rectangle and label the sides with the binomials:
Next, we fill in the rectangle with the appropriate terms:
Finally, we read off the product:
xy - 2x + 3y - 6
This is an example of the FOIL method for binomial multiplication, where FOIL stands for
First, Outer, Inner, Last.
Equations and Inequalities
Algebra is also used to solve equations and inequalities. An equation is a statement that
two expressions are equal, while an inequality is a statement that one expression is
greater than or less than another expression.
For example, the following are all equations:
2x + 3 = 7
x^2 - 4 = 0
(x + 2)(x - 3) = 0
To solve an equation, we need to find the value(s) of the variable(s) that make the
equation true.
