factorisation using identities 49x^2+ 4y^2 copy me likh bhejo answer
Answers
Factorisation- The chapter lays emphasis on the concept of how to express algebraic expressions as the products of their factors.
In the introduction part following topics are discussed:
- Factors of natural numbers
- Factors of algebraic expressions
- An irreducible factor is a factor that cannot be expressed further as a product of factors.
The chapter gives detail about the following topics:
What is Factorisation?
When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.
After this, the Method of Common Factors is explained.
A systematic way of factorising an expression is the common factor method. It contains three steps.
Another section deals with a method called Factorising by regrouping terms. To practice questions based on this method, unsolved exercise 14.1 is given.
Now the question arises What is Regrouping?
- Rearranging the expression allows us to form groups leading to factorisation. This is called regrouping.
- Factorisation using identities and factors in the form of (x +a) (x+b) are explained.
- Division of Algebraic Expressions: This section is divided into the following sub-sections:
a.).Division of a monomial by another monomial
b).. Division of a polynomial by a monomial
Division of algebraic expressions continued ( Polynomial ÷ Polynomial)
Division is the inverse of multiplication.
Can You Find the Error?
Important statements mentioned in the section:
➡Remember to make use of brackets, while substituting a negative value.
Remember, when you multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).
➡Coefficient 1 of a term is usually not shown. But while adding like terms, we include it in the sum.
Remember, when you square a monomial, the numerical coefficient and each factor has to be squared.
➡While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.
Identity used:- (a+b)^2 = a^2 + 2ab + b^2
(49 x + 4y) ^ 2 = 2401x^2 + 2 * 49x * 4y + 16y^2
= 49x (49x + 4) + 4y( 49x + 4y)
Ans = (49x + 4) (49x + 4y)