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MATHEMATICS

JAMB 2004 - Question 13

Mathematics 2004 JAMB Past Questions - Question 13: factorize completely ac – 2bc - a² + 4b²

factorize completely ac – 2bc - a² + 4b²

A: (a-2b)(c+a-2b)

B: (a-2b)(c-a-2b)

C: (a-2b)(c+a+2b)

D: (a-2b)(c-a+2b)

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Correct Answer

Explanation

To factorize the expression ac - 2bc - a² + 4b², we can look for common factors and use factoring techniques.Rearranging the terms, we have:ac - 2bc - a² + 4b²Taking out common factors, we can factor by grouping:c(a - 2b) - (a² - 4b²)Now, let's focus on the second part, which is a difference of squares:c(a - 2b) - (a + 2b)(a - 2b)Now, we have a common factor of (a - 2b) in both terms. Factoring it out, we get:(a - 2b)(c - (a + 2b))Therefore, the completely factored form of ac - 2bc - a² + 4b² is (a - 2b)(c - (a + 2b)).