Solve Algebra Assignment Question in 15 Seconds | Instant Calculation Techniques

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Our experts who have been providing the best algebra assignment help have brought you this blog with some amazing tricks and shortcuts to solve algebra assignments in no time. But, before we jump into that section, let’s take an insight into what is algebra.

Overview of Algebra

Algebra is a branch of mathematics that deals with number theory, geometry and analysis. It is used to study algebraic structures and solve equations. Though the roots of this subject can be traced to ancient Babylonians, works of Francois Viete contributed a lot to modern algebra. Now, we shall look into some streams of algebra that students usually get assignments from their professors.

What Are Different Streams of Algebra?

Here we listed out 3 top streams of algebra.

1.Elementary Algebra

This includes the basic concepts and formulas of algebra. It is usually taught at the high school level.

2.Linear Algebra

This is the study of linear sets of equations and their transformation properties.

3.Abstract Algebra

This is known as the modern algebra that deals with algebraic structures such as rings, groups, vectors, sets, etc.

These are the three different streams of algebra and its applications. Now, we shall understand how to solve algebra.

How to Solve Algebra Equations Using Simple Tricks?

Before we begin with solving algebraic equations, we shall look into ‘what are the basics of algebra’. This is because once we brush up our basics, then it can facilitate in easily solving any problem.

What Are the Basics of Algebra?

The above image includes a list of basic algebra formulas that can help in solving any algebra equation.

Here in the below section, we listed out some tricks along with examples to solve any algebraic equation in just seconds. So, lets get started...

Question 1: If the value of a + b + c= 0, then find the value of   a²⁄bc + b²⁄ca + c²⁄ab

In this question, the usual process takes 7-8 steps to get the desired answer. But, here we will solve this equation using the substitution method and calculate the same answer.

Trick: For the above expression, come up with a number combination which after substitution will add up to zero.

1. We choose  a= 2, b= -1, c= -1
   
   
2. Now, it satisfies our given equation as well:  2-1-1 = 0
   
   
3. Substituting the given values in the expression –  a²⁄bc + b²⁄ca + c²⁄ab
   [2²/ (-1) (1)] + [(-1)²/ (-1) (2)] + [(-1)²/ (-1) (2)]
   
   
4. On solving the above equation further: (4/1) + (-1/2) + (-1/2) = 3

So, this is a simple 4-step process that can help you solve any problem in just 5-10 seconds.

Question 2: If  a²+b²=1 and c²+d²=2

Then find the value of (ac+bd)²+(ad-bc)²

Trick: Say, the equation is equivalent to E.

E=(ac+bd)²+(ad-bc)²

1. First, we shall solve the square of the equation.
   

   E=(a²c²+2adcd+b²d²)+(a²d²-2adcd+b²c²)

2. From the above equation, we can cancel out 2abcd with the opposite signs.
   

   E=(a²s²+b²d²)+(a²d²+b²c²)

3. Now, we will bring together the common terms for applying the principle of collection of friendly terms.
   

   E=(a²c²+a²d²)+b²c²+b²d²

4. Now, take out the common terms and club the likes together.
   

   E=a²(c²+d²)+b²(c²+d²)

5. Now, applying substitution:
   

   E=2(a²+b²)=2

So, these are the two major tricks that you can apply in any of your algebra assignment questions and can easily solve it within a few seconds. When you use these simple tricks, you can observe that it hardly takes 15 seconds to solve any complex algebraic problem. Now, that you know how to solve an algebraic equation, you can also befriend the ‘x’ in algebra and impress your professor easily.

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