Simplify the following:
16 (2 x-7)^2-25 (y+2)^2
16 (2 x-7)^2-25 (y+2)^2 = (4 (2 x-7))^2-(5 (y+2))^2:
(4 (2 x-7))^2-(5 (y+2))^2
Factor the difference of two squares. (4 (2 x-7))^2-(5 (y+2))^2 = (4 (2 x-7)-5 (y+2)) (4 (2 x-7)+5 (y+2)):
(4 (2 x-7)-5 (y+2)) (4 (2 x-7)+5 (y+2))
4 (2 x-7) = 8 x-28:
(4 (2 x-7)-5 (y+2)) (8 x-28+5 (y+2))
5 (y+2) = 5 y+10:
(4 (2 x-7)-5 (y+2)) (-28+8 x+5 y+10)
Grouping like terms, -28+8 x+10+5 y = 5 y+8 x+(10-28):
5 y+8 x+(10-28) (4 (2 x-7)-5 (y+2))
10-28 = -18:
(4 (2 x-7)-5 (y+2)) (5 y+8 x+-18)
4 (2 x-7) = 8 x-28:
(8 x-28-5 (y+2)) (5 y+8 x-18)
-5 (y+2) = -10-5 y:
(-28+8 x+-10-5 y) (5 y+8 x-18)
Grouping like terms, -28+8 x-10-5 y = -5 y+8 x+(-28-10):
-5 y+8 x+(-28-10) (5 y+8 x-18)
-28-10 = -38:
Answer: |
| (-5 y+8 x+-38) (5 y+8 x-18)