(a-1)(a^2-2a+1) solve using formula
answer in steps
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Answer:
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Step-by-step explanation:
a^3-b^3
✩ Question ✩
(a-1)(a²-2a+1) Solve using formula. Answer in steps.
✩ To find ✩
(a-1)(a²-2a+1)
✩ Formulae to be used ✩
☞ (x-y)² = (x²+2xy+y²)
☞ (x-y)² = (x³-3x²y+3xy²-y²)
✩ Solution ✩
Here, take x as a and y as 1.
(a-1)(a²-2a+1)
↝(a-1){a²-(2×a×1)+1²}
↝(a-1)(a-1)²
↝ a³-3a²1+3a×1²-1³
↝(a-1)³
✩ Hence ✩
(a-1)(a²-2a+1) = (a+1)³
✩ Therefore ✩
The value of (a-1)(a²-2a+1) is (a+1)³.
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✧ Some more formulae ✧
☞ (a+b)² = a²+2ab+b²
☞ (a-b)² = a²-2ab+b²
☞ a²-b² = (a+b)(a-b)
☞ a²+b² = (a+b)²-2ab
☞ a²+b² = (a-b)²+2ab
☞ 2(a²+b²) = (a+b)²+(a-b)²
☞ (a+b)³ = a³+3a²b+3ab²+b³
☞ (a-b)³ = a³-3a²b+3ab²-b³
☞ a³+b³ = (a+b)(a²-ab+b²)
☞ a³-b³ = (a-b)(a²+ab+b²)
๑ Hope this helps you. ๑