Question

factorise (a^2 - 3a)(a^2 - 3a -7) + 10

Answer 1

Given (a²-3a)(a²-3a-7) + 10

Let x = a² - 3a ---(1)(

Now ,

(a²-3a)(a²-3a-7) + 10

= x( x - 7 ) + 10

= x² - 7x + 10

/* Splitting the middle term,we get */

= x² - 2x - 5x + 10

= x( x - 2 ) - 5( x - 2 )

= ( x - 2 )( x - 5 )

= ( a² - 3a - 2 ) ( a² - 3a - 5 ) [ From (1) ]

Therefore.,

$\red { (a^{2} - 3a ) ( a^{2} - 3a - 7 ) + 10 }$

$\green {= (a^{2} - 3a - 2)( a^{2} - 3a - 5 ) }$

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