Algebra for grade 8.

For grade 8

Operation on expressions:
Like arithmetic expressions we can perform various operations on algebraic expressions. They include addition, subtraction, multiplication and division. The order to be followed is same as in arithmetic. That is;
Division first
Multiplication second
Addition / Subtraction last.
See more (link to grade 7)

Use of brackets & expressions:
We use brackets to change the order of operations according to our requirements.
For this we have different kinds of brackets. They are;
1. "___" Bar bracket.
2. "( )" Parenthesis bracket (also called round bracket or small bracket).
3. "{ }" Braces (also called flower bracket or curly bracket or medium bracket).
4. "[ ]" square bracket (also called big bracket).
We first of all solve bar bracket then small then medium and then big.

Example:                             ____
Simplify , a - [ 3a + { 2a - ( 2a - a + 2 )}]
= a - [ 3a + { 2a - ( 2a - a - 2 )}]
due to minus sign out side the bar bracket the sign is changed.
= a - [ 3a + { 2a - ( a - 2 )}]
= a - [ 3a + { 2a - a + 2 }]
again signs of 2 and a are changed due to minus sign.
= a - [ 3a + { a + 2 }]
= a - [ 3a + a + 2 ]
= a - [ 4a + 2 ]
= a - 4 a - 2
= - 3 a - 2 , It is the simplified expression.

Use of formulae in algebra:
We use many formulas in algebra to avoid detailed calculations. A formula is a generalized form of some specific expression. In short we use formulae as short cuts.

Some frequently used formulae:
1. ( a + b )2 = ( a + b ) ( a + b )
= a ( a + b ) + b ( a + b )
= a2 +ab + ab + b2
= a2 + 2ab + b2, so we generalize,
( a + b )2 = a2 + 2ab + b2
Example:
· Find ( a + 3 )2
= a2 +2.a.3 +32
= a2 +6a + 9.
It was easy to calculate it with formula.
· Find the value of (104)2
= (100 + 4)2
= (100)2 + 2(100)(4) + (4)2
= 10000 + 800 + 16
= 10816
With the help of formula we do not have to use calculator for calculating such a big calculation.
2. ( a - b )2 = (a - b) ( a - b )
= a (a - b ) - b ( a - b )
= a2 - ab - ab + b2
= a2 - 2ab + b2
( a - b )2 = a2 - 2ab + b2
Example:
· Find (94)2
= (100 - 6 )2
= (100)2 - 2 (100)(6) + (6)2
= 10000 - 600 + 36
= 10036 - 600
= 9436
3. ( a + b )2 = (a - b)2 + 4ab
4. ( a - b )2 = (a + b)2 - 4ab
5. ( a - b ) (a + b ) = a2 - b2
6. ( x + a ) ( x + b ) = x2 + (a + b ) x +ab
All these formulae can be proved by simple steps as first two are proved. And are used, like first few examples, to simplify the calculation.

Back