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Mind-Blowing Math Algebra Formula Tricks

Mind-Blowing Math Algebra Formula Tricks

Algebra problems With Solutions

Example 1: Solve, (x-1)2 = [4√(x-4)]2
Solution: x
2-2x+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 


(i) 12 + 2x

(ii) 6y

(iii) z-25


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)= 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



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:



 Math Algebra Formula

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

 Math Algebra Formula

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,


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