xcube-8y+1+6xy plz tell this factorisations
Answers
terms or numbers to get one term or number.
Examples for multiplication are given below:
Ex1: 3*3=9
Ex2: 2a*a=2a2
The Process of writing an algebraic expression as a product of two or more expressions is called factorization.
We know that, FACTORIZATION is exactly opposite of multiplication.
Let us study factorization, by simple examples…
Ex1: Write the factors of 6.
6 = 2*3 (factors of any number must be in its simplest form)
So, 2 and 3 are the factors of 6.
Ex2: Write the factors of 10x
10x = 2*5*x
So, the factors of 10x are 2, 5 and x.
We can also take 1 as a factor of any given expression. But it does not give anything new.
Ex1: write the factors of a+8
(a+8)=1*(a+8)
This is called trivial factorization.
DIFFERENT METHODS OF FACTORIZATION – FactorizationThere are many ways of factorizing a given expression. Let us study them one by one in brief.
Factorization taking common factors:In this type of factorization we need to take common factors of a given expressions and them we need to simplify and write it again.
Example1: Write the factors of 5x2 -10x
Ans:
5x2 -10x = 5*x*x-2*5*x
= 5*x*(x-2)
=5x(x-2)
[Note for Example1: Write the factors of 5x2 -10x
Step (i): write the factors of each term
5x2 = 5*x*x
10x=2*5*x
Step (ii): Substitute the factors each term in the given expression.
5x2 -10x = 5*x*x-2*5*x
Step (iii): take the common factor outside the bracket.
5x2 -10x = 5*x*(x-2)
=5x(x-20)]
Example2: factorize 4a+12b.
Ans:
4a+12b = 4*a+3*4*b
= 4*(a+3*b)
=4(a+3b)
Note for Example2: Write the factors of 4a+12b
Step (i): write the factors of each term
4a=4*a
12b=3*4*b
Step (ii): Substitute the factors each term in the given expression.
4a+12b = 4*a+3*4*b
Step (iii): take the common factor outside the bracket.
4a+12b= 4*(a+3*b)
=4(a+3b)
Example3: Factorise 3x2y-6xy2+9xy
Ans:
3x2y-6xy2+9xy= 3*x*x*y-2*3*x*y*y+3*3*x*y
=3*x*y*(x-2y+3)
=3xy(x-2y+3)
Example4: Factorise a3-a2+a.
Ans: