# Writing Equivalent Polynomial Expressions

Directions: Use the digits 1-9, at most one time each, to create a true statement.

### Hint

ex. 3+4 = 2+5

Number of Unique Solutions: 168
1: 1x^2 + 6x^3 + 3x^2 – 2x^3 = 9x^2 + 4x^3 – 5x^2
2: 1x^2 + 6x^3 + 3x^2 – 4x^3 = 9x^2 + 2x^3 – 5x^2
3: 1x^2 + 6x^3 + 5x^2 – 2x^3 = 9x^2 + 4x^3 – 3x^2
4: 1x^2 + 6x^3 + 5x^2 – 4x^3 = 9x^2 + 2x^3 – 3x^2
5: 1x^2 + 7x^3 + 2x^2 – 3x^3 = 8x^2 + 4x^3 – 5x^2
6: 1x^2 + 7x^3 + 2x^2 – 3x^3 = 9x^2 + 4x^3 – 6x^2
7: 1x^2 + 7x^3 + 2x^2 – 4x^3 = 8x^2 + 3x^3 – 5x^2
8: 1x^2 + 7x^3 + 2x^2 – 4x^3 = 9x^2 + 3x^3 – 6x^2
9: 1x^2 + 7x^3 + 3x^2 – 2x^3 = 8x^2 + 5x^3 – 4x^2
10: 1x^2 + 7x^3 + 3x^2 – 5x^3 = 8x^2 + 2x^3 – 4x^2
11: 1x^2 + 7x^3 + 4x^2 – 2x^3 = 8x^2 + 5x^3 – 3x^2
12: 1x^2 + 7x^3 + 4x^2 – 5x^3 = 8x^2 + 2x^3 – 3x^2
13: 1x^2 + 7x^3 + 5x^2 – 3x^3 = 8x^2 + 4x^3 – 2x^2
14: 1x^2 + 7x^3 + 5x^2 – 4x^3 = 8x^2 + 3x^3 – 2x^2
15: 1x^2 + 7x^3 + 6x^2 – 3x^3 = 9x^2 + 4x^3 – 2x^2
16: 1x^2 + 7x^3 + 6x^2 – 4x^3 = 9x^2 + 3x^3 – 2x^2
17: 1x^2 + 8x^3 + 2x^2 – 3x^3 = 7x^2 + 5x^3 – 4x^2
18: 1x^2 + 8x^3 + 2x^2 – 3x^3 = 9x^2 + 5x^3 – 6x^2
19: 1x^2 + 8x^3 + 2x^2 – 5x^3 = 7x^2 + 3x^3 – 4x^2
20: 1x^2 + 8x^3 + 2x^2 – 5x^3 = 9x^2 + 3x^3 – 6x^2
21: 1x^2 + 8x^3 + 3x^2 – 2x^3 = 9x^2 + 6x^3 – 5x^2
22: 1x^2 + 8x^3 + 3x^2 – 6x^3 = 9x^2 + 2x^3 – 5x^2
23: 1x^2 + 8x^3 + 4x^2 – 3x^3 = 7x^2 + 5x^3 – 2x^2
24: 1x^2 + 8x^3 + 4x^2 – 5x^3 = 7x^2 + 3x^3 – 2x^2
25: 1x^2 + 8x^3 + 5x^2 – 2x^3 = 9x^2 + 6x^3 – 3x^2
26: 1x^2 + 8x^3 + 5x^2 – 6x^3 = 9x^2 + 2x^3 – 3x^2
27: 1x^2 + 8x^3 + 6x^2 – 3x^3 = 9x^2 + 5x^3 – 2x^2
28: 1x^2 + 8x^3 + 6x^2 – 5x^3 = 9x^2 + 3x^3 – 2x^2
29: 1x^2 + 9x^3 + 2x^2 – 3x^3 = 7x^2 + 6x^3 – 4x^2
30: 1x^2 + 9x^3 + 2x^2 – 3x^3 = 8x^2 + 6x^3 – 5x^2
31: 1x^2 + 9x^3 + 2x^2 – 4x^3 = 6x^2 + 5x^3 – 3x^2
32: 1x^2 + 9x^3 + 2x^2 – 5x^3 = 6x^2 + 4x^3 – 3x^2
33: 1x^2 + 9x^3 + 2x^2 – 6x^3 = 7x^2 + 3x^3 – 4x^2
34: 1x^2 + 9x^3 + 2x^2 – 6x^3 = 8x^2 + 3x^3 – 5x^2
35: 1x^2 + 9x^3 + 3x^2 – 2x^3 = 8x^2 + 7x^3 – 4x^2
36: 1x^2 + 9x^3 + 3x^2 – 4x^3 = 6x^2 + 5x^3 – 2x^2
37: 1x^2 + 9x^3 + 3x^2 – 5x^3 = 6x^2 + 4x^3 – 2x^2
38: 1x^2 + 9x^3 + 3x^2 – 7x^3 = 8x^2 + 2x^3 – 4x^2
39: 1x^2 + 9x^3 + 4x^2 – 2x^3 = 8x^2 + 7x^3 – 3x^2
40: 1x^2 + 9x^3 + 4x^2 – 3x^3 = 7x^2 + 6x^3 – 2x^2
41: 1x^2 + 9x^3 + 4x^2 – 6x^3 = 7x^2 + 3x^3 – 2x^2
42: 1x^2 + 9x^3 + 4x^2 – 7x^3 = 8x^2 + 2x^3 – 3x^2
43: 1x^2 + 9x^3 + 5x^2 – 3x^3 = 8x^2 + 6x^3 – 2x^2
44: 1x^2 + 9x^3 + 5x^2 – 6x^3 = 8x^2 + 3x^3 – 2x^2
45: 2x^2 + 6x^3 + 3x^2 – 1x^3 = 9x^2 + 5x^3 – 4x^2
46: 2x^2 + 6x^3 + 3x^2 – 5x^3 = 9x^2 + 1x^3 – 4x^2
47: 2x^2 + 6x^3 + 4x^2 – 1x^3 = 9x^2 + 5x^3 – 3x^2
48: 2x^2 + 6x^3 + 4x^2 – 5x^3 = 9x^2 + 1x^3 – 3x^2
49: 2x^2 + 7x^3 + 1x^2 – 3x^3 = 8x^2 + 4x^3 – 5x^2
50: 2x^2 + 7x^3 + 1x^2 – 3x^3 = 9x^2 + 4x^3 – 6x^2
51: 2x^2 + 7x^3 + 1x^2 – 4x^3 = 8x^2 + 3x^3 – 5x^2
52: 2x^2 + 7x^3 + 1x^2 – 4x^3 = 9x^2 + 3x^3 – 6x^2
53: 2x^2 + 7x^3 + 3x^2 – 1x^3 = 9x^2 + 6x^3 – 4x^2
54: 2x^2 + 7x^3 + 3x^2 – 6x^3 = 9x^2 + 1x^3 – 4x^2
55: 2x^2 + 7x^3 + 4x^2 – 1x^3 = 9x^2 + 6x^3 – 3x^2
56: 2x^2 + 7x^3 + 4x^2 – 6x^3 = 9x^2 + 1x^3 – 3x^2
57: 2x^2 + 7x^3 + 5x^2 – 3x^3 = 8x^2 + 4x^3 – 1x^2
58: 2x^2 + 7x^3 + 5x^2 – 4x^3 = 8x^2 + 3x^3 – 1x^2
59: 2x^2 + 7x^3 + 6x^2 – 3x^3 = 9x^2 + 4x^3 – 1x^2
60: 2x^2 + 7x^3 + 6x^2 – 4x^3 = 9x^2 + 3x^3 – 1x^2
61: 2x^2 + 8x^3 + 1x^2 – 3x^3 = 7x^2 + 5x^3 – 4x^2
62: 2x^2 + 8x^3 + 1x^2 – 3x^3 = 9x^2 + 5x^3 – 6x^2
63: 2x^2 + 8x^3 + 1x^2 – 5x^3 = 7x^2 + 3x^3 – 4x^2
64: 2x^2 + 8x^3 + 1x^2 – 5x^3 = 9x^2 + 3x^3 – 6x^2
65: 2x^2 + 8x^3 + 3x^2 – 1x^3 = 9x^2 + 7x^3 – 4x^2
66: 2x^2 + 8x^3 + 3x^2 – 7x^3 = 9x^2 + 1x^3 – 4x^2
67: 2x^2 + 8x^3 + 4x^2 – 1x^3 = 9x^2 + 7x^3 – 3x^2
68: 2x^2 + 8x^3 + 4x^2 – 3x^3 = 7x^2 + 5x^3 – 1x^2
69: 2x^2 + 8x^3 + 4x^2 – 5x^3 = 7x^2 + 3x^3 – 1x^2
70: 2x^2 + 8x^3 + 4x^2 – 7x^3 = 9x^2 + 1x^3 – 3x^2
71: 2x^2 + 8x^3 + 6x^2 – 3x^3 = 9x^2 + 5x^3 – 1x^2
72: 2x^2 + 8x^3 + 6x^2 – 5x^3 = 9x^2 + 3x^3 – 1x^2
73: 2x^2 + 9x^3 + 1x^2 – 3x^3 = 7x^2 + 6x^3 – 4x^2
74: 2x^2 + 9x^3 + 1x^2 – 3x^3 = 8x^2 + 6x^3 – 5x^2
75: 2x^2 + 9x^3 + 1x^2 – 4x^3 = 6x^2 + 5x^3 – 3x^2
76: 2x^2 + 9x^3 + 1x^2 – 5x^3 = 6x^2 + 4x^3 – 3x^2
77: 2x^2 + 9x^3 + 1x^2 – 6x^3 = 7x^2 + 3x^3 – 4x^2
78: 2x^2 + 9x^3 + 1x^2 – 6x^3 = 8x^2 + 3x^3 – 5x^2
79: 2x^2 + 9x^3 + 3x^2 – 4x^3 = 6x^2 + 5x^3 – 1x^2
80: 2x^2 + 9x^3 + 3x^2 – 5x^3 = 6x^2 + 4x^3 – 1x^2
81: 2x^2 + 9x^3 + 4x^2 – 3x^3 = 7x^2 + 6x^3 – 1x^2
82: 2x^2 + 9x^3 + 4x^2 – 6x^3 = 7x^2 + 3x^3 – 1x^2
83: 2x^2 + 9x^3 + 5x^2 – 3x^3 = 8x^2 + 6x^3 – 1x^2
84: 2x^2 + 9x^3 + 5x^2 – 6x^3 = 8x^2 + 3x^3 – 1x^2
85: 3x^2 + 6x^3 + 1x^2 – 2x^3 = 9x^2 + 4x^3 – 5x^2
86: 3x^2 + 6x^3 + 1x^2 – 4x^3 = 9x^2 + 2x^3 – 5x^2
87: 3x^2 + 6x^3 + 2x^2 – 1x^3 = 9x^2 + 5x^3 – 4x^2
88: 3x^2 + 6x^3 + 2x^2 – 5x^3 = 9x^2 + 1x^3 – 4x^2
89: 3x^2 + 6x^3 + 4x^2 – 1x^3 = 9x^2 + 5x^3 – 2x^2
90: 3x^2 + 6x^3 + 4x^2 – 5x^3 = 9x^2 + 1x^3 – 2x^2
91: 3x^2 + 6x^3 + 5x^2 – 2x^3 = 9x^2 + 4x^3 – 1x^2
92: 3x^2 + 6x^3 + 5x^2 – 4x^3 = 9x^2 + 2x^3 – 1x^2
93: 3x^2 + 7x^3 + 1x^2 – 2x^3 = 8x^2 + 5x^3 – 4x^2
94: 3x^2 + 7x^3 + 1x^2 – 5x^3 = 8x^2 + 2x^3 – 4x^2
95: 3x^2 + 7x^3 + 2x^2 – 1x^3 = 9x^2 + 6x^3 – 4x^2
96: 3x^2 + 7x^3 + 2x^2 – 6x^3 = 9x^2 + 1x^3 – 4x^2
97: 3x^2 + 7x^3 + 4x^2 – 1x^3 = 9x^2 + 6x^3 – 2x^2
98: 3x^2 + 7x^3 + 4x^2 – 2x^3 = 8x^2 + 5x^3 – 1x^2
99: 3x^2 + 7x^3 + 4x^2 – 5x^3 = 8x^2 + 2x^3 – 1x^2
100: 3x^2 + 7x^3 + 4x^2 – 6x^3 = 9x^2 + 1x^3 – 2x^2
101: 3x^2 + 8x^3 + 1x^2 – 2x^3 = 9x^2 + 6x^3 – 5x^2
102: 3x^2 + 8x^3 + 1x^2 – 6x^3 = 9x^2 + 2x^3 – 5x^2
103: 3x^2 + 8x^3 + 2x^2 – 1x^3 = 9x^2 + 7x^3 – 4x^2
104: 3x^2 + 8x^3 + 2x^2 – 7x^3 = 9x^2 + 1x^3 – 4x^2
105: 3x^2 + 8x^3 + 4x^2 – 1x^3 = 9x^2 + 7x^3 – 2x^2
106: 3x^2 + 8x^3 + 4x^2 – 7x^3 = 9x^2 + 1x^3 – 2x^2
107: 3x^2 + 8x^3 + 5x^2 – 2x^3 = 9x^2 + 6x^3 – 1x^2
108: 3x^2 + 8x^3 + 5x^2 – 6x^3 = 9x^2 + 2x^3 – 1x^2
109: 3x^2 + 9x^3 + 1x^2 – 2x^3 = 8x^2 + 7x^3 – 4x^2
110: 3x^2 + 9x^3 + 1x^2 – 4x^3 = 6x^2 + 5x^3 – 2x^2
111: 3x^2 + 9x^3 + 1x^2 – 5x^3 = 6x^2 + 4x^3 – 2x^2
112: 3x^2 + 9x^3 + 1x^2 – 7x^3 = 8x^2 + 2x^3 – 4x^2
113: 3x^2 + 9x^3 + 2x^2 – 4x^3 = 6x^2 + 5x^3 – 1x^2
114: 3x^2 + 9x^3 + 2x^2 – 5x^3 = 6x^2 + 4x^3 – 1x^2
115: 3x^2 + 9x^3 + 4x^2 – 2x^3 = 8x^2 + 7x^3 – 1x^2
116: 3x^2 + 9x^3 + 4x^2 – 7x^3 = 8x^2 + 2x^3 – 1x^2
117: 4x^2 + 6x^3 + 2x^2 – 1x^3 = 9x^2 + 5x^3 – 3x^2
118: 4x^2 + 6x^3 + 2x^2 – 5x^3 = 9x^2 + 1x^3 – 3x^2
119: 4x^2 + 6x^3 + 3x^2 – 1x^3 = 9x^2 + 5x^3 – 2x^2
120: 4x^2 + 6x^3 + 3x^2 – 5x^3 = 9x^2 + 1x^3 – 2x^2
121: 4x^2 + 7x^3 + 1x^2 – 2x^3 = 8x^2 + 5x^3 – 3x^2
122: 4x^2 + 7x^3 + 1x^2 – 5x^3 = 8x^2 + 2x^3 – 3x^2
123: 4x^2 + 7x^3 + 2x^2 – 1x^3 = 9x^2 + 6x^3 – 3x^2
124: 4x^2 + 7x^3 + 2x^2 – 6x^3 = 9x^2 + 1x^3 – 3x^2
125: 4x^2 + 7x^3 + 3x^2 – 1x^3 = 9x^2 + 6x^3 – 2x^2
126: 4x^2 + 7x^3 + 3x^2 – 2x^3 = 8x^2 + 5x^3 – 1x^2
127: 4x^2 + 7x^3 + 3x^2 – 5x^3 = 8x^2 + 2x^3 – 1x^2
128: 4x^2 + 7x^3 + 3x^2 – 6x^3 = 9x^2 + 1x^3 – 2x^2
129: 4x^2 + 8x^3 + 1x^2 – 3x^3 = 7x^2 + 5x^3 – 2x^2
130: 4x^2 + 8x^3 + 1x^2 – 5x^3 = 7x^2 + 3x^3 – 2x^2
131: 4x^2 + 8x^3 + 2x^2 – 1x^3 = 9x^2 + 7x^3 – 3x^2
132: 4x^2 + 8x^3 + 2x^2 – 3x^3 = 7x^2 + 5x^3 – 1x^2
133: 4x^2 + 8x^3 + 2x^2 – 5x^3 = 7x^2 + 3x^3 – 1x^2
134: 4x^2 + 8x^3 + 2x^2 – 7x^3 = 9x^2 + 1x^3 – 3x^2
135: 4x^2 + 8x^3 + 3x^2 – 1x^3 = 9x^2 + 7x^3 – 2x^2
136: 4x^2 + 8x^3 + 3x^2 – 7x^3 = 9x^2 + 1x^3 – 2x^2
137: 4x^2 + 9x^3 + 1x^2 – 2x^3 = 8x^2 + 7x^3 – 3x^2
138: 4x^2 + 9x^3 + 1x^2 – 3x^3 = 7x^2 + 6x^3 – 2x^2
139: 4x^2 + 9x^3 + 1x^2 – 6x^3 = 7x^2 + 3x^3 – 2x^2
140: 4x^2 + 9x^3 + 1x^2 – 7x^3 = 8x^2 + 2x^3 – 3x^2
141: 4x^2 + 9x^3 + 2x^2 – 3x^3 = 7x^2 + 6x^3 – 1x^2
142: 4x^2 + 9x^3 + 2x^2 – 6x^3 = 7x^2 + 3x^3 – 1x^2
143: 4x^2 + 9x^3 + 3x^2 – 2x^3 = 8x^2 + 7x^3 – 1x^2
144: 4x^2 + 9x^3 + 3x^2 – 7x^3 = 8x^2 + 2x^3 – 1x^2
145: 5x^2 + 6x^3 + 1x^2 – 2x^3 = 9x^2 + 4x^3 – 3x^2
146: 5x^2 + 6x^3 + 1x^2 – 4x^3 = 9x^2 + 2x^3 – 3x^2
147: 5x^2 + 6x^3 + 3x^2 – 2x^3 = 9x^2 + 4x^3 – 1x^2
148: 5x^2 + 6x^3 + 3x^2 – 4x^3 = 9x^2 + 2x^3 – 1x^2
149: 5x^2 + 7x^3 + 1x^2 – 3x^3 = 8x^2 + 4x^3 – 2x^2
150: 5x^2 + 7x^3 + 1x^2 – 4x^3 = 8x^2 + 3x^3 – 2x^2
151: 5x^2 + 7x^3 + 2x^2 – 3x^3 = 8x^2 + 4x^3 – 1x^2
152: 5x^2 + 7x^3 + 2x^2 – 4x^3 = 8x^2 + 3x^3 – 1x^2
153: 5x^2 + 8x^3 + 1x^2 – 2x^3 = 9x^2 + 6x^3 – 3x^2
154: 5x^2 + 8x^3 + 1x^2 – 6x^3 = 9x^2 + 2x^3 – 3x^2
155: 5x^2 + 8x^3 + 3x^2 – 2x^3 = 9x^2 + 6x^3 – 1x^2
156: 5x^2 + 8x^3 + 3x^2 – 6x^3 = 9x^2 + 2x^3 – 1x^2
157: 5x^2 + 9x^3 + 1x^2 – 3x^3 = 8x^2 + 6x^3 – 2x^2
158: 5x^2 + 9x^3 + 1x^2 – 6x^3 = 8x^2 + 3x^3 – 2x^2
159: 5x^2 + 9x^3 + 2x^2 – 3x^3 = 8x^2 + 6x^3 – 1x^2
160: 5x^2 + 9x^3 + 2x^2 – 6x^3 = 8x^2 + 3x^3 – 1x^2
161: 6x^2 + 7x^3 + 1x^2 – 3x^3 = 9x^2 + 4x^3 – 2x^2
162: 6x^2 + 7x^3 + 1x^2 – 4x^3 = 9x^2 + 3x^3 – 2x^2
163: 6x^2 + 7x^3 + 2x^2 – 3x^3 = 9x^2 + 4x^3 – 1x^2
164: 6x^2 + 7x^3 + 2x^2 – 4x^3 = 9x^2 + 3x^3 – 1x^2
165: 6x^2 + 8x^3 + 1x^2 – 3x^3 = 9x^2 + 5x^3 – 2x^2
166: 6x^2 + 8x^3 + 1x^2 – 5x^3 = 9x^2 + 3x^3 – 2x^2
167: 6x^2 + 8x^3 + 2x^2 – 3x^3 = 9x^2 + 5x^3 – 1x^2
168: 6x^2 + 8x^3 + 2x^2 – 5x^3 = 9x^2 + 3x^3 – 1x^2

### Check Also

Directions: Directions: Using the integers from −9 to 9 at most once each, place one …

1. There is a typo in the answer. The “-1x^2” should be “-1x^3.”

2. Here are the ones my students came up with:

5x^2 + 7x^3 + 1x^2 – 3x^3 = 8x^2 + 4x^3 – 2x^2

4x^2 + 7x^3 + 3x^2 – 6x^3 = 9x^2 + 1x^3 – 2x^2

3x^2 + 6x^3 + 4x^2 – 1x^3 = 9x^2 + 5x^3 – 2x^2

2x^2 + 9x^3 + 5x^2 – 6x^3 = 8x^2 + 3x^3 – 1x^2

4x^2 + 3x^3 + 5x^2 – 2x^3 = 9x^2 + 1x^3 – 0x^2

5x^2 + 4x^3 + 2x^2 – 3x^3 = 7x^2 + 1x^3 – 0x^2

3x^2 + 6x^3 + 5x^2 – 2x^3 = 8x^2 + 4x^3 – 0x^2

1x^2 + 9x^3 + 2x^2 – 4x^3 = 6x^2 + 5x^3 – 3x^2

3x^2 + 6x^3 + 4x^2 – 5x^3 = 9x^2 + 1x^3 – 2x^2

1x^2 + 9x^3 + 2x^2 – 5x^3 = 3x^2 + 4x^3 – 0x^2

3. 4x^2 + 8x^3 + 3x^2 – 7x^3 = 9x^2 + 1x^3 – 2x^2

4. 4x^2 + 8x^3 + 3x^2 – 7x^3 = 9x^2 + 1x^3 – 2x^2

My 6th grade challenge class and I figured this out