STD - 10 MATHS CHAPTER - 3 ALGEBRA

 Samacheer Kalvi Syllabus 10th Maths Solutions 

Chapter 3 : Algebra

STD - 10 Maths Chapter – 3 : Algebra [ இயற்கணிதம் ] Published By : P.Thirukumaresakani M.A.,M.Sc.,B.Ed., GGHSS, KONGANAPURAM, SALEM DT.

Introduction Of Algebra:-

Algebra is the branch of maths that uses alphabetical letters to find unknown numbers. These letters are also called variables. The values which are known in the given expression such as numbers are called constants. Algebra involves the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables.

இயற்கணிதம் என்பது அறியப்படாத எண்களைக் கண்டறிய அகரவரிசை எழுத்துக்களைப் பயன்படுத்தும் கணிதத்தின் கிளை ஆகும். இந்த எழுத்துக்கள் மாறிகள் என்றும் அழைக்கப்படுகின்றன. எண்கள் போன்ற கொடுக்கப்பட்ட வெளிப்பாட்டில் அறியப்படும் மதிப்புகள் மாறிலிகள் எனப்படும். இயற்கணிதம் என்பது மாறிலிகள் மற்றும் மாறிகள் இரண்டையும் உள்ளடக்கிய கூட்டல், கழித்தல், பெருக்கல் மற்றும் வகுத்தல் போன்ற கணிதத்தின் எளிய செயல்பாட்டை உள்ளடக்கியது.

Algebra Identities:-

·         (a + b)² = a² + 2ab + b²

·         (a - b)² = a² - 2ab + b²

·         (a + b)(a - b) = a² - b²

·         (a + b)³ = a³ +3a²b + 3ab² + b³

·         (a - b)³ = a³ - 3a²b + 3ab² - b³

·         (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

 PROPERTIES OF ALGEBRA:-

 Algebra follows the same set of rules as Number Systems. The order of operations is preserved, and the laws governing addition and multiplication still apply.

However, with the inclusion of variables comes a new set of challenges. For a definitive value for an expression, we need to evaluate an algebraic expression for specific values of the variables, observe how the value of the expression changes as the values of the variables changes.

Like operations with numbers, operations with variables obey certain laws.

Commutative law for addition & multiplication:-

Associative law for addition & multiplication:-

Both the commutative law and the associative law apply to either addition or multiplication, but not with both operations together.

The distributive law deals with the combination of addition and multiplication. When a sum is multiplied by value, the value is distributed to each part of the sum.

STD-10 MATHS CHAPTER - 3 :
ALGEBRA EXERCISE VIDEOS GIVEN BELOW:-

The following video gives a clear and concise understanding of Algebra.All students should download the following exercise videos.

 You can write the answers  and check the exercises video in the following below videos.

கீழ்கண்ட வீடியோவில் இயற்கணிதம்  பற்றி தெளிவாகவும் விளக்கமாகவும்  புரிந்து கொள்ளும் வகையில் கொடுக்கப் பட்டுள்ளது. இதை  மாணவ மாணவியர்கள் அனைவரும் கீழ்க்கண்ட     video  வை பதிவிறக்கம் செய்து கொள்ளவும். 

EXERCISE : 3.1 Q.NO - 1 [i]

EXERCISE : 3.1 Q.NO - 1 [ii]

EXERCISE : 3.1 Q.NO - 1 [iii]

EXERCISE : 3.1 Q.NO - 3

EXERCISE : 3.1 Q.NO - 4

EXERCISE : 3.1 Q.NO - 5

EXERCISE : 3.1 FULL VIDEO

EXERCISE : 3.2 Q.NO - 1 [ i ]

EXERCISE : 3.2 Q.NO - 1 [ ii ]

EXERCISE : 3.2 Q.NO - 1 [ iii ]

EXERCISE : 3.2 Q.NO - 1 [ iv ]

EXERCISE : 3.2 Q.NO - 2 [ i , ii , iii ]

EXERCISE : 3.2 Q.NO - 2 [ iv ]

EXERCISE : 3.2 Q.NO - 2 [ v ]

EXERCISE : 3.2 Q.NO - 2 [ vi ]

EXERCISE : 3.2 FULL VIDEO Uploaded Soon

EXERCISE : 3.3 Q.NO - 1 [ i ]

EXERCISE : 3.3 Q.NO - 1 [ ii ]

EXERCISE : 3.3 Q.NO - 1 [ iii ]

EXERCISE : 3.3 Q.NO - 2 [ i ]

EXERCISE : 3.3 Q.NO - 2 [ ii ]

EXERCISE : 3.3 Q.NO - 3 [ i ]

EXERCISE : 3.3 Q.NO - 3 [ ii ]

EXERCISE : 3.3 Q.NO - 4 [ i ]

EXERCISE : 3.3 Q.NO - 4 [ ii ]

EXERCISE 3.3 FULL VIDEO Uploaded Soon

EXERCISE : 3.4 Q.NO - 1 [ i , ii , iii , iv ]