Question

4x²-a²+2a-1 factories it please explain in a paper​

Answer 1

Step-by-step explanation:

a²-2a+1 can be written as (a-1)²

after this ,you can easily factorise it

Answer 2

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\: {4x}^{2} - {a}^{2} + 2a - 1$

$\rm \: \: = \: \: {4x}^{2} - \bigg( {a}^{2} - 2a + 1\bigg)$

$\rm \: \: = \: \: {4x}^{2} - \bigg( {a}^{2} - 2a + {(1)}^{2} \bigg)$

$\rm \: \: = \: \: {4x}^{2} - \bigg( {a}^{2} - 2 \times a \times 1 + {(1)}^{2} \bigg)$

$\rm \: \: = \: \: {4x}^{2} - {(a - 1)}^{2}$

$\: \: \: \: \: \: \: \red{ \: \bigg\{ \: \sf \because \: {x}^{2} - 2xy + {y}^{2} = {(x - y)}^{2} \: \bigg \}}$

$\rm \: \: = \: \: {(2x)}^{2} - {(a - 1)}^{2}$

$\rm \: \: = \: \: (2x - a + 1)(2x + a - 1)$

$\: \: \: \: \: \: \: \red{ \: \bigg\{ \: \sf \because \: {x}^{2} - {y}^{2} = {(x - y)}(x + y)\: \bigg \}}$

Hence,

$\red{\boxed{\rm\:{4x}^{2}-{a}^{2}+2a-1 = (x + 2a - 1)(x - 2a + 1)}}$

Concept Used :-

1. Method of Common Factors

• In this method, we have to write the irreducible factors of all the terms

• Then find the common factors amongst all the irreducible factors.

• The required factor form is the product of the common term we had chosen and the left over terms.

2. Factorisation by Regrouping Terms

Sometimes it happens that there is no common term in the expressions then

• We have to make the groups of the terms.

• Then choose the common factor among these groups.

• Find the common binomial factor and it will give the required factors.

3. Factorization by using Identities

• Sometimes the above methods are not helpful in Factorization. In such cases we use method of factorization using Identities.

Identities are as follow :-

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

• (a + b)² + (a - b)² = 2(a² + b²)

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)