Question bank / Equivalent expressions
Math · Advanced Math Medium
Which expression is equivalent to ( 2 x − 3 ) 2 (2x - 3)^2 ( 2 x − 3 ) 2
A 4 x 2 − 12 x + 9 4x^2 - 12x + 9 4 x 2 − 12 x + 9
B 4 x 2 − 6 x + 9 4x^2 - 6x + 9 4 x 2 − 6 x + 9
D 4 x 2 − 12 x − 9 4x^2 - 12x - 9 4 x 2 − 12 x − 9
Show answer and explanation Answer: A
Use ( a − b ) 2 = a 2 − 2 a b + b 2 (a - b)^2 = a^2 - 2ab + b^2 ( a − b ) 2 = a 2 − 2 ab + b 2 a = 2 x a = 2x a = 2 x b = 3 b = 3 b = 3 ( 2 x ) 2 − 2 ( 2 x ) ( 3 ) + 3 2 = 4 x 2 − 12 x + 9 (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9 ( 2 x ) 2 − 2 ( 2 x ) ( 3 ) + 3 2 = 4 x 2 − 12 x + 9
Choice C squares each term separately and drops the middle term − 12 x -12x − 12 x
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