Mind-Blowing Math Algebra Formula Tricks
Algebra problems With Solutions
Example 1: Solve,
(x-1)2 =
[4√(x-4)]2
Solution: x2-2x+1 = 16(x-4)
x2-2x+1 = 16x-64
x2-18x+65 = 0
(x-13) x (x-5) = 0
Hence, x = 13 and x =
5.
Algebra Problems for Class 6
In class 6, students
will be introduced with an algebra concept. Here, you will learn how the
unknown values are represented in terms of variables. The given
expression can be solved only if we know the value of unknown variable. Let us
see some examples.
Example: Solve, 4x + 5
when, x = 3.
Solution: Given, 4x +
5
Now putting the value
of x=3, we get;
4 (3) + 5 = 12 + 5 =
17.
Example: Give
expressions for the following cases:
(i) 12 added to 2x
(ii) 6 multiplied by y
(iii) 25 subtracted
from z
(iv) 17 times of
m
Solution:
(i) 12 + 2x
(ii) 6y
(iii) z-25
(iv)17m
Algebra Problems for Class 7
In class 7, students
will deal with algebraic expressions like x+y, xy, 32x2-12y2, etc. There are different kinds of the
terminology used in case algebraic equations such as;
- Term
- Factor
- Coefficient
Let us understand
these terms with an example. Suppose 4x + 5y is an algebraic expression, then
4x and 5y are the terms. Since here the variables used are x and y, therefore,
x and y are the factors of 4x + 5y. And the numerical factor attached to the
variables are the coefficient such as 4 and 5 are the coefficient of x and y in
the given expression.
Any expression with
one or more terms is called a polynomial. Specifically, a
one-term expression is called a monomial; a two-term expression is called
a binomial, and a three-term expression is called a trinomial.
Terms which have the
same algebraic factors are like terms. Terms which have different
algebraic factors are unlike terms. Thus, terms 4xy and – 3xy are
like terms; but terms 4xy and – 3x are not like terms.
Example: Add 3x + 5x
Solution: Since 3x and
5x have the same algebraic factors, hence, they are like terms and can be added
by their coefficient.
3x + 5x = 8x
Example: Collect
like terms and simplify the expression: 12x2 – 9x + 5x – 4x2 – 7x + 10.
Solution: 12x2 – 9x + 5x – 4x2 – 7x + 10
= (12 – 4)x2 – 9x + 5x – 7x + 10
= 8x2 – 11x + 10
Algebra Problems for Class 8
Here, students will
deal with algebraic identities. See the examples.
Example: Solve (2x+y)2
Solution: Using the
identity: (a+b)2 = a2 + b2 + 2 ab, we get;
(2x+y) = (2x)2 + y2 + 2.2x.y = 4x2 + y2 + 4xy
Example: Solve (99)2 using algebraic identity.
Solution: We can
write, 99 = 100 -1
Therefore, (100 – 1 )2
= 1002 + 12 – 2 x 100 x 1 [By identity: (a -b)2 = a2 + b2 – 2ab
= 10000 + 1 – 200
= 9801
Algebra Problems
Question 1: There
are 47 boys in the class. This is three more than four times the number of
girls. How many girls are there in the class?
Solution: Let the
number of girls be x
As per the given
statement,
4 x + 3 = 47
4x = 47 – 3
x = 44/4
x = 11
Question 2: The sum of
two consecutive numbers is 41. What are the numbers?
Solution: Let one of
the numbers be x.
Then the other number
will x+1
Now, as per the given
questions,
x + x + 1 = 41
2x + 1 = 41
2x = 40
x = 20
So, the first number
is 20 and second number is 20+1 = 21
Linear Algebra
Problems
There are various
methods For Solving the Linear Equations
- Cross multiplication method
- Replacement method or
Substitution method
- Hit and trial method
Math Algebra Formula
There are Variety of
different Algebra problem present and are solved depending upon their
functionality and state. For example, a linear equation problem can’t be solved
using a quadratic equation formula and vice verse for, e.g., x+x/2=7 then solve
for x is an equation in one variable for x which can be satisfied by only one
value of x. Whereas x2+5x+6 is a quadratic equation which is
satisfied for two values of x the domain of algebra is huge and vast so for
more information.
Math Algebra Formula
Introduction
Algebra often brings back memories of confusing
equations and mind-numbing calculations, but what if I told you that there are
mind-blowing algebra tricks that can make this subject not only manageable but
also enjoyable? In this article, we will explore three important algebraic
techniques that will change the way you approach math forever. Get ready to
unleash your inner mathematician and impress your friends with these
mind-boggling algebra tricks!
Factorization Magic
One of the most powerful algebraic tricks is
factorization. By breaking down complex expressions into simpler forms,
factorization not only simplifies calculations but also unveils hidden patterns
and relationships. Let's dive into some mind-blowing factorization techniques:
Perfect Square Trinomials
Imagine encountering a quadratic expression that
seems impossible to factorize. Fear not! Perfect square trinomials come to the
rescue. These special quadratic expressions can be factored into a square of a
binomial. For example, consider the expression x^2 + 6x + 9. By recognizing it
as a perfect square trinomial, we can rewrite it as (x + 3)^2. This
factorization method saves time, reduces errors, and showcases the elegance of
algebra.
Difference of Squares
Another mind-blowing factorization trick lies in
recognizing the difference of squares. When confronted with an expression in
the form a^2 - b^2, where 'a' and 'b' represent any real numbers, we can factorize
it into (a + b)(a - b). For instance, if we have x^2 - 4, we can express it as
(x + 2)(x - 2). This simple technique reveals a hidden symmetry within the
expression and unlocks new possibilities for further simplification.
Grouping Method
The grouping method is a fantastic technique for
factorizing expressions consisting of four terms. By identifying common factors
within pairs of terms, we can group them together and factor out a common
binomial. For instance, if we have the expression x^2 + 3x + 2x + 6, we can
group the terms as (x^2 + 3x) + (2x + 6) and factor out common terms to get x(x
+ 3) + 2(x + 3). Finally, we factor out the common binomial (x + 3) to obtain
the simplified form of (x + 2)(x + 3). The grouping method not only simplifies
complex expressions but also enhances our problem-solving abilities.
Equations that Solve Themselves Math Algebra Formula
Finding the solution to an equation can often be a
daunting task. However, there are algebraic tricks that can make the process
feel like magic. Let's explore some mind-blowing equation-solving techniques:
Cross-Multiplication
When confronted with a linear equation involving
fractions, cross-multiplication can save the day. Instead of going through the
tedious process of finding common denominators, we can simply cross-multiply
the numerator of one fraction with the denominator of the other. For example,
if we have the equation 2/3 = x/6, we can cross-multiply to solve for 'x' by
getting 3x = 12. By dividing both sides by 3, we find that x = 4. This elegant
technique eliminates the need for unnecessary steps and speeds up the
equation-solving process.
Squaring Both Sides
In some cases, equations may involve square roots,
which can complicate the solving process. However, squaring both sides of the
equation can simplify matters. By performing this manipulation, we eliminate
the square root and transform the equation into a simpler form. For instance,
if we have the equation √(3x + 1) = 2, we can square both sides to obtain 3x +
1 = 4. This new equation can be readily solved using basic algebraic
techniques. Just remember to verify the solutions obtained, as squaring both
sides can introduce extraneous solutions.
Zero Product Property
Another remarkable trick in algebra involves the
Zero Product Property. This property states that if two factors multiply to
zero, then at least one of the factors must be zero. This concept enables us to
solve quadratic equations by factoring them and setting each factor equal to
zero. For example, if we have the quadratic equation x^2 + 5x + 6 = 0, we can
factor it as (x + 2)(x + 3) = 0. Applying the Zero Product Property, we find
that x + 2 = 0 or x + 3 = 0, leading to the solutions x = -2 and x = -3. This
powerful technique simplifies the process of finding solutions to quadratic
equations and introduces a touch of mathematical elegance.
Beyond the Limits
Algebra is not just about solving equations and
simplifying expressions. It has the power to push the boundaries of our
mathematical understanding. Let's explore some mind-blowing algebraic concepts
that will take your mathematical journey to the next level:
Complex Numbers Math Algebra Formula
When faced with the challenge of taking the square
root of a negative number, algebra introduces us to the concept of complex
numbers. Complex numbers consist of a real part and an imaginary part, where
the imaginary unit 'i' is defined as the square root of -1. This mind-boggling
notion allows us to work with previously unsolvable equations, such as √(-9).
By representing it as 3i,
