Factorise 5a^(2)+8ab-4b^(2)

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Factorise  5a^(2)+8ab-4b^(2)

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Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is 5a^2 + 8ab - 4b^2. Here, the coefficient of a^2 is 5, the coefficient of ab is 8, and the coefficient of b^2 is -4.Find Multiplying Numbers: Look for two numbers that multiply to ac (the product of the coefficient of a^2 and the coefficient of b^2) and add up to b (the coefficient of ab). In this case, ac = 5 * (-4) = -20 and b = 8. We need to find two numbers that multiply to -20 and add up to 8. The numbers 10 and -2 satisfy these conditions because 10 * (-2) = -20 and 10 + (-2) = 8.Rewrite Middle Term: Rewrite the middle term using the two numbers found in Step 2. We can express 8ab as 10ab - 2ab. So, the expression becomes 5a^2 + 10ab - 2ab - 4b^2.Factor by Grouping: Factor by grouping. Group the terms into two pairs: (5a^2 + 10ab) and (-2ab - 4b^2). Factor out the greatest common factor from each pair. From the first pair, we can factor out 5a, giving us 5a(a + 2b). From the second pair, we can factor out -2b, giving us -2b(a + 2b).Write Factored Form: Write the factored form. Both groups now have a common factor of (a + 2b). Factor this out to get the final factored form: (5a - 2b)(a + 2b).

Factorise $5 a^{2}+8 a b-4 b^{2}$

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Factorise $5 a^{2}+8 a b-4 b^{2}$