Question: What is the a3+b3 formula:
- (a+b)(a2-ab+b2)
- (a-b)(a2+ab+b2)
- a3+b3-3ab(a+b)
- a3+b3+3ab(a+b)
Answer: (A) (a+b)(a2-ab+b2)
a3+b3 Formula Solution:
The formula for a3+b3 can be derived using the following steps:
- Start with the following identity:
(a+b)3 = a3 + 3a2b + 3ab2 + b3
- Expand the left-hand side of the equation using the perfect cube factorization method:
(a+b)3 = (a+b)(a2+2ab+b2)
- Subtract a3 and b3 from both sides of the equation:
(a+b)3 - a3 - b3 = (a+b)(a2+2ab+b2) - a3 - b3
- Factor out a common factor of (a+b) on the right-hand side of the equation:
(a+b)(a2+2ab+b2) - a3 - b3 = (a+b)(a2+2ab+b2 - a2 - ab - b2)
- Simplify the expression on the right-hand side of the equation:
(a+b)(a2+2ab+b2 - a2 - ab - b2) = (a+b)(a2-ab+b2)
Therefore, the formula for a3+b3 is (a+b)(a2-ab+b2).
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