Question

factorise:
1) 144-a^6
2) b^4-a^2
3) 3x^3 y- 243 xy^3
4) a^4 - 81
5) x^4 - y^4

Answer 1

1) 144 - a⁶ 

= (12)² - (a³)²

= (12 + a³) (12 - a³)

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2) b⁴ - a²

= (b²)² - a²

= (b² + a) (b² - a) 

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3) 3x³y - 243 xy³

= 3xy(x² - 81y²)

= 3xy[(x)² - (9y)²)]

= 3xy[(x+9y)(x-9y)]

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4) a⁴ - 81

= (a²)² - 9²

= (a² + 9) (a² - 9) 

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5) x⁴  - y⁴

= (x²)² - (y²)²

= (x² - y²) (x² + y²) 

=(x + y) (x - y) (x² +y²)
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