Evaluate with explanation. (a²+b²) (a+b) (a-b)
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QUESTION : Evaluate with explanation. (a²+b²) (a+b) (a-b)
WHAT TO FIND : THE VALUE OF (a²+b²)(a+b)(a-b)
SOLUTION :
ON THE BASIS OF THE FORMULA a²-b² = (a+b) (a-b)
WE CAN WRITE : (a²+b²)(a²-b²)
=a²×a²+a²×-b²+b²×a²+b²×-b²
=a^4+-ab²-b^4×ab²×-b^4
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*Question:—
Evaluate with explanation. (a²+b²) (a+b) (a-b).
*Answer:—
→ (a² + b²) (a + b) (a - b)
→ (a² + b²) (a² - b²)
→ a²(a² - b²) + b²(a² - b²)
→ a⁴ - a²b² + a²b² - b⁴
→ a⁸ - a⁴b⁴ + a⁴b⁴ - b⁸
→ (a⁴ - b⁴)
Hence our answer is (a⁴ - b⁴).
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