Algebra

Simplify the following:
4 x (x + 2) - 2 x (3 - x)

 

Factor 2 out of 4 x (x + 2) - 2 (3 - x) x giving 2 (2 x (x + 2) - (3 - x) x):
2 (2 x (x + 2) - (3 - x) x)

2 x (x + 2) = 2 x^2 + 4 x:
2 (2 x^2 + 4 x - (3 - x) x)

-x (3 - x) = x^2 - 3 x:
2 (x^2 - 3 x + 2 x^2 + 4 x)

 

Grouping like terms, 4 x + 2 x^2 - 3 x + x^2 = (2 x^2 + x^2) + (4 x - 3 x):
2 ((2 x^2 + x^2) + (4 x - 3 x))

2 x^2 + x^2 = 3 x^2:
2 (3 x^2 + (4 x - 3 x))

4 x - 3 x = x:
2 (3 x^2 + x) = 6x^2  +  2x

 

4x(x + 2) - 2x (3 - x)

 

4x^2 + 8x - 6x + 2x^2

(4x^2 + 2x^2) + (8x - 6x)

6x^2  +  2x