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Factorise fully quad40-2b^(2)

Factorise fully 40−2b2 \quad 40-2 b^{2}

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Full solution

Q. Factorise fully 40−2b2 \quad 40-2 b^{2}
  1. Factor out common factor: First, notice that both terms have a common factor of 22. Let's factor that out.\newlineCalculation: 2(20−b2)2(20 - b^2)
  2. Rewrite as difference of squares: Now we have a difference of squares, since 2020 isn't a perfect square, let's rewrite it as 4×54\times5 to make it easier.\newlineCalculation: 2(4×5−b2)2(4\times5 - b^2)
  3. Recognize perfect squares: Recognize that 4×54\times 5 can be written as (2×5)2(2\times\sqrt{5})^2, and b2b^2 is already a perfect square.\newlineCalculation: 2((2×5)2−b2)2((2\times\sqrt{5})^2 - b^2)
  4. Factor difference of squares: Now we can factor the difference of squares.\newlineCalculation: 2((25−b)(25+b))2((2\sqrt{5} - b)(2\sqrt{5} + b))
  5. Combine for final form: Combine everything to get the final factored form.\newlineCalculation: 2(25−b)(25+b)2(2\sqrt{5} - b)(2\sqrt{5} + b)

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