Students can go through AP Board 8th Class Maths Notes Chapter 11 Algebraic Expressions to understand and remember the concepts easily.
AP State Board Syllabus 8th Class Maths Notes Chapter 11 Algebraic Expressions
→ There are number of situations in which we need to multiply algebraic expressions.
→ A monomial multiplied by a monomial always gives a monomial.
→ While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the monomial.
→ In carrying out the multiplication of an algebraic expression with another algebraic expression (monomial/ binomial/ trinomial etc.) we multiply term by term i.e. every term of the expression is multiplied by every term in the another expression.
→ An identity is an equation, which is true for-all values of the variables in the equation. On the other hand, an equation is true only for certain values of its variables. An equation is not an identity.
→ The following are identities:
I. (a + b)2 = a2 + 2ab + b2
II. (a – b)2 = a2 – 2ab + b2
III. (a + b) (a -b) = a2 – b2
IV. (x + a) (x + b) = x2 + (a + b)x + ab
→ The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.
Note:
We know that
(+) × (+) = +
(+) × (-) = –
(-) × (+) = –
(-) × (-) = +