Question

lcm 3a2-5ab-12b2,a5-27a2b2,9a2+24ab+16b2​

Answer 1

SOLUTION

TO DETERMINE

The LCM of 3a² - 5ab -12b² , $\sf{ {a}^{5} - 27 {a}^{2} {b}^{3} }$ , 9a² + 24ab + 16b²

EVALUATION

First expression

= 3a² - 5ab -12b²

= 3a² - 9ab + 4ab - 12b²

= 3a (a - 3b) + 4b ( a - 3b)

= ( 3a + 4b ) ( a - 3b )

Second expression

$\sf{ = {a}^{5} - 27 {a}^{2} {b}^{3} }$

= a² ( a³ - 27b³ )

= a² ( a - 3b )( a² + 3ab + 9b² )

Third expression

= 9a² + 24ab + 16b²

= (3a) ² + 2 × 3a × 4b + (4b)²

= ( 3a + 4b )²

Hence the required LCM

= a²( a - 3b )( a² + 3ab + 9b² ) ( 3a + 4b )²

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