{"id":6140,"date":"2020-02-21T19:20:28","date_gmt":"2020-02-21T13:50:28","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=6140"},"modified":"2022-11-04T12:06:28","modified_gmt":"2022-11-04T06:36:28","slug":"algebra-formulas-for-class-8","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/algebra-formulas-for-class-8\/","title":{"rendered":"Algebra Formula for Class 8"},"content":{"rendered":"\n

Algebra consists of the following topics in Class 8 .
(a) Linear equation
(b) Laws of Exponents
(c) Algebraic Expressions and Identities
(d) Factorization
Here are Algebra Formula for Class 8 topic wise<\/p>\n\n\n\n

Linear Equation<\/h2>\n\n\n\n

What is Linear equation in one Variable<\/strong><\/p>\n\n\n\n

We will restrict the\nabove equation with two conditions<\/p>\n\n\n\n

(a) algebraic equation in one variable
(b) variable will have power 1 only <\/p>\n\n\n\n

or<\/p>\n\n\n\n

An equation of the form ax + b = 0, where a and b are real numbers, such that a is not equal to zero, is called a linear equation in one variables<\/p>\n\n\n\n

Linear equation in One variable has only one Solution. It can be solved as given below<\/p>\n\n\n\n

\"Linear<\/figure>\n\n\n\n

Laws Of Exponents<\/h2>\n\n\n\n

Here are the laws of exponents when a <\/em>and b <\/em>are\nnon-zero integers and m<\/em>, n <\/em>are any integers.<\/p>\n\n\n\n

a-m<\/sup> = 1\/am<\/sup> <\/p>\n\n\n\n

am<\/sup> \/ an<\/sup> = am-n<\/sup> <\/p>\n\n\n\n

(am<\/sup> )n<\/sup>     =\namn<\/sup> <\/p>\n\n\n\n

am<\/sup> x bm <\/sup> = (ab)m<\/sup> <\/p>\n\n\n\n

am<\/sup> \/ bm <\/sup>  = (a\/b)m<\/sup>\n<\/p>\n\n\n\n

a0<\/sup> =1<\/p>\n\n\n\n

(a\/b)-m<\/sup> =(b\/a)m<\/sup> <\/p>\n\n\n\n

(1)n<\/sup> <\/em>= 1 for infinitely many n<\/em>. (-1)p<\/sup> =1  for any even integer p <\/p>\n\n\n\n

Algebraic Expressions and Identities<\/h2>\n\n\n\n

Algebraic expression<\/strong>
It is the expression having constants and variable. It can have multiple variable and multiple power of the variable<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Types<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Operation on Algebraic Expressions<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Algebraic Identities<\/strong><\/p>\n\n\n\n

(a <\/em>+ b<\/em>)2<\/sup> = a2<\/sup><\/em> + 2ab <\/em>+ b2<\/sup><\/em>
(a <\/em>– b<\/em>)2<\/sup> = a2<\/sup><\/em> – 2ab <\/em>+ b2<\/sup><\/em>
 (a <\/em>+ b<\/em>) (a <\/em>\u2013 b<\/em>) = a2<\/sup><\/em>\u2013 b2<\/sup><\/em>
(x <\/em>+ a<\/em>) (x <\/em>+ b<\/em>) = x2<\/sup><\/em> + (a <\/em>+ b<\/em>) x <\/em>+ ab <\/em>
(x <\/em>+ a<\/em>) (x <\/em>– b<\/em>) = x2<\/sup><\/em> + (a <\/em>– b<\/em>) x <\/em>– ab <\/em>
(x <\/em>– a<\/em>) (x <\/em>+ b<\/em>) = x2<\/sup><\/em> + (b -a<\/em>) x <\/em>– ab <\/em>
(x <\/em>– a<\/em>) (x <\/em>– b<\/em>) = x2<\/sup><\/em> -(a <\/em>+ b<\/em>) x <\/em>+ ab <\/em> <\/p>\n\n\n\n

Factorisation<\/h2>\n\n\n\n

Factorisation of algebraic expression<\/strong>
When we factorise an algebraic expression, we write it as a product of factors. These
factors may be numbers, algebraic variables or algebraic expressions
The expression 6x <\/em>(x <\/em>– 2). It can be written as a product of factors.
2,3, x <\/em>and (x <\/em>– 2)
$6x <\/em>(x <\/em>– 2) =2 \\times 3 \\times x<\/em> \\times (x <\/em>– 2)$
The factors 2,3, x <\/em>and (x <\/em>+2) are irreducible factors of 6x <\/em>(x <\/em>+ 2).<\/p>\n\n\n\n

Method of Factorisation<\/strong><\/p>\n\n\n\n

\"Algebra<\/figure>\n\n\n\n

Division of algebraic expression<\/strong><\/p>\n\n\n\n

Division of algebraic expression is performed by Factorisation of both the numerator and denominator and then cancelling the common factors.
Steps of Division<\/strong>
(1) Identify the Numerator and denominator
(2) Factorise both the Numerator and denominator by the technique of Factorisation using common factor, regrouping, identities and splitting
(3) Identify the common factor between numerator and denominator
(4) Cancel the common factors and finalize the result<\/p>\n\n\n\n

Example<\/strong>
$\\frac {48 (x^2yz+ xy^2z+ xyz^2)}{4xyz}$
$=\\frac {48xyz (x + y + z)}{4xyz}$
$= 12 (x + y + z)$<\/p>\n\n\n\n

Here Dividend=48 (x2<\/sup>yz <\/em>+ xy2<\/sup>z <\/em>+ xyz2<\/sup><\/em>)
Divisor=4xyz<\/em>
Quotient=<\/em>12 (x <\/em>+ y <\/em>+ z<\/em>)
So, we have
Dividend = Divisor \u00d7 Quotient.
In general, however, the relation is
Dividend = Divisor \u00d7 Quotient + Remainder
When reminder is not zero<\/p>\n\n\n\n

Hope you like the post on Algebra Formula for Class 8.<\/p>\n\n\n\n

Also Reads<\/p>\n\n\n\n