Question

Two sets of quadratic expressions are shown below in various forms:

Answer 1

Solution:

1. $x^2 + 3 x +2= x^2 + 2 x + x + 2= x(x+2)+1(x+2)=(x+1)(x+2)\\\\ x^2 + 3 x + 2=(x+\frac{3}{2})^2-(\frac{3}{2})^2+2=(x+\frac{3}{2})^2-2.25+2=(x+\frac{3}{2})^2-0.25$

2. $x^2 + 5 x + 6 =x^2+ 3 x + 2 x+6=x(x+3)+2(x+3)= (x + 2)(x + 3)\\\\ x^2 + 5 x + 6 =(x+\frac{5}{2})^2-(\frac{5}{2})^2+6=(x+\frac{5}{2})^2-6.25+6=(x+\frac{5}{2})^2-0.25$

Line 1:  x² + 3 x + 2= (x + 1)(x + 2)= (x + 1.5)² − 0.25 contains three equivalent expressions.

Answer 2

Line one is equivalent