Question

factorise 3a^7-192ab^6​

Answer 1

Step-by-step explanation:

Given:

$3 {a}^{7} - 192a {b}^{6}$

To find: Factors

Solution:

By analysis ,one can see that 3a is common in both terms

$3a( {a}^{6} - 64 {b}^{6} )$

Now,

Manipulate the terms in bracket

$3a[ ({a}^{3} )^{2} - ((2b)^{3} )^{2}]$

Apply identity:

$\bold{\green{{x}^{2} - {y}^{2} = (x + y)(x - y)}}$

Thus,

$3a( {a}^{3} - 8 {b}^{3} )({a}^{3} + 8 {b}^{3})$

Apply identity:

$\bold{\pink{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}} \\ \\ \bold{\purple{{x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )}}$

Thus,

$3a( a + 2b)( {a}^{2} - 2ab + 4 {b}^{2} )( a - 2b)( {a}^{2} + 2ab + 4 {b}^{2} )$

Factorisation of

${a}^{7} - 192a {b}^{6} = 3a( a + 2b)(a - 2b)\\( {a}^{2} - 2ab + 4 {b}^{2} ) ( {a}^{2} + 2ab + 4 {b}^{2} )$

Hope it helps you.

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