Question

factorise: 18ab³-8a³b​

Answer 1

Answer:

-2ab (2a+3b)(2a-3b)

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Step-by-step explanation:

18ab³-8a³b

Write in standard form:

-8a³b+18ab³

rewrite 18ab³ as - (- 18ab³)

-8a³b - (-18ab³)

factor out -1

-(8a³b-18ab³)

factor out common terms

-2ab(4a²-9b²)

rewrite: 4 as 2² and 9 as 3²

-2ab ( 2²a² - 3²b²)

Apply exponent rules: (a)^m (b)^m = (ab)^m

-2ab ( (2a)² - (3b)²)

Apply difference of two square formula:

a²-b² = (a+b)(a-b)

Well,

(2a²)- (3b)² = (2a+3b)(2a-3b)

-2ab (2a+3b)(2a-3b)

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