Question

Factorise:-5(2a-3b)²-20(3a-b)²​

Answer 1

Answer:

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5(2a-3b)²-20(3a-b)²

Step-by-step explanation:

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Answer 2

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Explanation:

$- 5 {(2a - 3b)}^{2} - 20 {(3a - b)}^{2}$

Identity used here :-

$\bold{\boxed{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}$

$= > - 5(4 {a}^{2} - 12ab + 9 {b}^{2} ) - 20 {(3a - b)}^{2}$

$= > - 20 {a}^{2} + 60ab - 45 {b}^{2} - 20(9 {a}^{2} - 6ab + {b}^{2} )$

$= > - 20 {a}^{2} + 60ab - 45 {b}^{2} - 180 {a}^{2} + 120ab - 20 {b}^{2}$

$= > ( - 20 - 180) {a}^{2} + (60 + 120)ab + ( - 45 - 20) {b}^{2}$

$= > - 200 {a}^{2} + 180ab - 65 {b}^{2}$

$= > - 200 {a}^{2} + 180ab - 65 {b}^{2}$

$\bold\fcolorbox{aqua}{orange}{Answer}$$\bold{ - 200 {a}^{2} + 180ab - 65 {b}^{2} }$