Question

Factorisation -

$\tt \pink{ {a}^{3}x - {a}^{2}b(x - y) - {ab}^{2} (y - z) - {b}^{3} z}$
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Answer 1

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

$\rm :\longmapsto\:{a}^{3}x - {a}^{2}b(x - y) - {ab}^{2} (y - z) - {b}^{3} z$

$\rm \:  = \: {a}^{3}x - {a}^{2}bx + {a}^{2}by - {ab}^{2}y + {ab}^{2} z - {b}^{3} z$

$\rm \:  =  \: {xa}^{2}(a - b) + aby(a - b) + {zb}^{2}(a - b)$

$\rm \:  =  \:  (a - b)( {xa}^{2} + aby + {zb}^{2})$

Hence,

Factorization of

$\bf :\longmapsto\:{a}^{3}x - {a}^{2}b(x - y) - {ab}^{2} (y - z) - {b}^{3} z$

$\rm \:  =  \:  (a - b)( {xa}^{2} + aby + {zb}^{2})$

Concept Used :-

1. Method of Common Factors

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

Then, we find the common factors amongst all the irreducible factors.

The required factor form is the product of the common term.

2. Factorisation by Regrouping Terms

Sometimes, it might 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.

Then, find the common factor and it will give the required factors.

Answer 2

Concept Used :-

1. Method of Common Factors

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

Then, we find the common factors amongst all the irreducible factors.

The required factor form is the product of the common term.

2. Factorisation by Regrouping Terms

Sometimes, it might 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.

Then, find the common factor and it will give the required factors.