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Answers
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
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)