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Algebra Formulas

A basic formula in Algebra represents the relationship between different variables. The variable could be taken as x, y, a, b, c or any other alphabet that represents a number unknown yet. Example – (x + y = z)

\[ x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\]
\[ x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\]
\[\mathbf{a_{1}x + b_{1}y + c_{1} = 0}\]
\[\mathbf{a_{2}x+ b_{2}y + c_{2}} = 0 \]
Distributive Property a ( b+c) = (a × b) + (a × c)
Commutative Property of Addition a + b = b+a
Commutative Property of Multiplication a× b = b×a
Associative Property of Addition a + (b + c ) = ( a+ b ) +c
Associative Property of Multiplication a ( b ×  c ) = ( a× b ) × c
Additive Identity Property a +0 = a
Multiplicative Identity Property a×1 = a
Additive Inverse Property a+ ( -a) = 0
Multiplicative Inverse Property a × 1/a = 1
Zero Property of Multiplication a × 0 = 0
If\[\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}\] then magnitude or length or norm or absolute value of \[\vec{a} \] is \[ \left | \overrightarrow{a} \right |=a=\sqrt{x^{2}+y^{2}+z^{2}}\]
A vector of unit magnitude is unit vector. If \[\vec{a}\] is a vector then unit vector of \[\vec{a}\] is denoted by \[\hat{a}\] and \[\hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\] Therefore \[ \hat{a}=\frac{\hat{a}}{\left | \hat{a} \right |}\hat{a}\]
Important unit vectors are \[\hat{i}, \hat{j}, \hat{k}\], where \[\hat{i} = [1,0,0],\: \hat{j} = [0,1,0],\: \hat{k} = [0,0,1]\]
If \[ l=\cos \alpha, m=\cos \beta, n=\cos\gamma,\] then \[ \alpha, \beta, \gamma,\] are called directional angles of the vectors\[\overrightarrow{a}\] and \[\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma = 1\]
\[\vec{a}+\vec{b}=\vec{b}+\vec{a}\]
\[\vec{a}+\left ( \vec{b}+ \vec{c} \right )=\left ( \vec{a}+ \vec{b} \right )+\vec{c}\]
\[k\left ( \vec{a}+\vec{b} \right )=k\vec{a}+k\vec{b}\]
\[\vec{a}+\vec{0}=\vec{0}+\vec{a}\], therefore <span class=”latex-for-amp”>\[ \vec{0}\] is the <a href=”https://byjus.com/maths/additive-identity-vs-multiplicative-identity/”>additive identity</a> in vector addition.
\[\vec{a}+\left ( -\vec{a} \right )=-\vec{a}+\vec{a}=\vec{0}\], therefore <span class=”latex-for-amp”>\[\vec{a}\]  is the inverse in vector addition.

Algebra Formula in Video

What is Algebra?

Algebra is a mathematical segment that replaces letters for the number. An algebraic equation is working as a scale where both sides represent the same things and numbers are taken as the constants. Algebra may include multiple mathematical terms like the real number, complex numbers, vectors, matrix, and many other forms.

what is Algebra

Further, algebra is broken down into parts – one is elementary algebra and the other is abstract algebra. The first one is suitable for medical, science, engineering, mathematics, or economics, etc. At the same time, the second type is suitable for advanced mathematics only.

A basic equation in Algebra is an expression that contains at least one variable that we need to calculate to find something unknown to you. Example – (x – 38 = 12). This is an algebraic equation where we need to calculate the unknown variable x.

Algebra Problems with a Solution

Algebra is used everywhere and it can be used for solving daily problems too when it comes to knowing about the unknown variable. Let us see how it works actually. Take an example where you are trying to calculate the balls you started the day with if you sold 38 but still 12 is remaining.

Here, the algebraic equation would be x-38 = 12. We are trying to calculate unknown variable x that will tell you how many balls you started your day. The solution to the problem is (x=50), it means you started your day with 50 balls.

Question 1: Find out the value of 52 – 32

Solution:
Using the formula a2 – b2 = (a – b)(a + b)
where a = 5 and b = 3
(a – b)(a + b)
= (5 – 3)(5 + 3)
= 2 ×× 8
= 16

Question 2: 
43 ×× 42 = ?

Solution:
Using the exponential formula (am)(an) = am+n
where a = 4
43 ×× 42
= 43+2
= 45
= 1024

Why Algebra Formula Needs?

Wondered how Algebra formulas are needed even outside your high school? In reality, they are used everywhere either it is related to bill payments, calculation of healthcare costs, your future investment, planning for a house on EMIs or budget management for your project, etc. A deep understanding of Algebra formulas or equations can develop critical thinking, makes your logics stronger, and enhances your problem-solving skills especially when you enter the workspace.

Ultimately, the person having a good understanding of Algebra had a greater opportunity of getting success in science, mathematics, engineering, economics, complex mathematics fields or any other tech-related fields, etc. We wish you a successful future ahead with the right skills and knowledge of various Algebraic equations or formulas.

You should remember all the algebra Formulas which helps you to solve algebra equations and easy to understand. You should also check the more Maths formulas which are the help to learn more. if you have any questions regarding algebra related and algebra equations, you should share your problem here for the solution.

Algebra Formulas By Class

Download Algebra Formula in PDF

Now, we are going to share Algebra Formulas in PDF file. You would like to download a PDF file of Algebra Formulas then click on the below link.

  • Download Algebra Formula in PDF

Summary of Algebra Formula

Andlearning.org is a single website that is sharing all Algebra formulas which is useful for math calculation. I checked numbers of websites that have shared Algebra formulas but we can’t find any website which has shared all Algebra formulas including all notes. If you have any questions regarding Algebra formulas please let me know through comment, mail, or social media. My expert team is waiting for your Algebra related doubts or questions for the solution.

 

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