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SAT Math Question And Step By Step Solution by originalKsp(m): 11:27am On Aug 15, 2016 |
SAT Question : Factorise completely 81a⁴ – 16b⁴ A.(3a + 2b) (2a – 3b) (9a² + 4b²) B.(3a – 2b) (2a – 3b) (4a² – 9b²) C.(3a – 2b) (3a + 2b) (9a² + 4b²) D.(3a – 2b) (2a – 3b) (9a² + 4b²) E.(3a – 2b) (2a – 3b) (9a²- 4b²) ******************* Solution ******************* Applying indices, 81a⁴ – 16b⁴ can be rewritten as (9a²)² – (4b²)² Applying difference of two squares (9a²)² – (4b²)² = (9a² – 4b²)(9a² + 4b²) Applying difference of two squares again: (9a² – 4b²)(9a² + 4b²) = ((3a)² – (2b)²)(9a² + 4b²) = (3a – 2b)(3a + 2b)(9a² + 4b²) The correct option is C SOURCE: http://samimath.com/q-and-a-factorisation/ ************************ ♦ Tutorial on difference of two squares is here http://samimath.com/difference-of-two-squares/ ♦Other step by step solution from samimath is here http://samimath.com/math-questions-and-solutions/ ************************* |
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