Question

drag a number into the box to create an equation that is true for all values of x. (2x + 3)^2-4x = 4x^2+□x + 9. options: 12, 16, 2, 6, 8

Explanation:

Step1: Expand left - hand side

Expand \((2x + 3)^2\) using \((a + b)^2=a^{2}+2ab + b^{2}\), where \(a = 2x\) and \(b = 3\). So \((2x+3)^2=(2x)^{2}+2\times(2x)\times3 + 3^{2}=4x^{2}+12x + 9\). Then \((2x + 3)^2-4x=4x^{2}+12x + 9-4x=4x^{2}+8x + 9\).

Answer:

8