Expand the following:
(5 t^2 - 2 w)^2
(5 t^2 - 2 w) (5 t^2 - 2 w) = (5 t^2) (5 t^2) + (5 t^2) (-2 w) + (-2 w) (5 t^2) + (-2 w) (-2 w):
5×5 t^2 t^2 - 2×5 t^2 w - 2×5 w t^2 - 2 (-2) w w
5 t^2×5 t^2 = 5×5 t^4:
5×5 t^4 - 2×5 t^2 w - 2×5 w t^2 - 2 (-2) w w
5×5 = 25:
25 t^4 - 2×5 t^2 w - 2×5 w t^2 - 2 (-2) w w
5 (-2) = -10:
25 t^4 + -10 t^2 w - 2×5 w t^2 - 2 (-2) w w
-2×5 = -10:
25 t^4 - 10 t^2 w + -10 w t^2 - 2 (-2) w w
-2 w (-2) w = -2 (-2) w^2:
25 t^4 - 10 t^2 w - 10 w t^2 + -2 (-2) w^2
-2 (-2) = 4:
Answer: |25 t^4 - 10 t^2 w - 10 w t^2 + 4 w^2
