Math, asked by balaji923, 2 months ago

please help me.
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Answers

Answered by DeepakUgalePatil
3

Answer:

please see that

Step-by-step explanation:

I am not your classmates so may be method is different but answer is helpful

brainiest please

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Answered by SƬᏗᏒᏇᏗƦƦᎥᎧƦ
36

Required answer :-

Question :

• Factorise the following:

(i) 8x³ + 125y³

(ii) 27x³ - 8y³

(iii) a⁶ - 64

Solution :

First understand the concept :-

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The sum or difference of two cubes

We know, a³-b³ = (a+b)³ - 3ab (a+b)

and, a³-b³ = (a-b)³ + 3ab(a- b)

Further a³+b³= (a+b)³ - 3ab (a+b)

= (a+b) [ (a+b)² - 3ab ]

= (a+b) (a²+2ab+b²-3ab)

= (a+b) (a²+2ab +b²-3ab)

= (a+b) (a²-ab+b²)

Similarly,

a³-b³ = (a²+ab+b²)

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Step by step explaination :-

(i) 8x³ + 125y³

→ (2x)³ + (5y)³

→ (2x + 5y) [ (2x)² - 2x*5y + (5y)² ]

→ (2x + 5y) (4x² - 10xy + 25y²)

(ii) 27x³ - 8y³

→ (3x)³ - (2y)³

→ (3x - 2y) [ (3x)² + 3x*2y + (2y)² ]

→ (3x - 2y) (9x² + 6xy + 4y²)

(iii) a⁶ - 64

→ a⁶ - 64

→ (a³)² - 8²

→ (a³ - 8) (a³- 8)

→ (a+ 2) (a²-2a+4) (a-2) (a²+2a+4)

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