Answer to Question #130581 in Algebra for Rimsha Ahmed

Question

• 4x² - 12x + 9 =
• 4(x² - 3x + (9/4)) =
• 4(x - 3/2)² + 0

Kindly, tell me how this Result "4(x - 3/2)² + 0" is obtained, please.

Thank you.

Answer 1

1 step. 4x² - 12x + 9 = 4(x² - 3x + (9/4))  factoring out 4. To do it, divide each coefficient by 4.

2 step. 4*(x² - 3x + (9/4)) = 4*(x - 3/2)² . According to the formula of full square: a² - 2*a*b + b² = (a - b)². 

In your example 'a' is 1, 'b' is 3/2. Then a² = 1, 2*a*b = 2*1*(3/2) = 3, b² = (3/2)² = 9/4

P.S. For every c : c+0 = c, so 0 can be cancelled in the answer.