Study this list of common errors carefully and identify any mistakes that you occasionally make. Note the numerical examples given.
| INCORRECT | CORRECT |
| (x + y)2 = x2 + y2 ? (3 + 2)2 = 32 + 22 = 13 ? |
(x + y)2 = x2 + 2xy + y2 (3 + 2)2 = 52 = 25 |
| ax × by = (ab)x+y ? 24 × 35 = (2 × 3)4+5 ? |
Cannot be simplified further (different bases and different exponents) |
| ax × ay = axy ? 54 × 53 = 512 ? |
ax·ay = ax+y 54 × 53 = 57 |
| (ax)y = a(x+y) ? (74)3 = 77 ? |
(ax)y = axy (74)3 = 712 |
| ax + ay = ax+y ? x3 + x2 = x5 ? |
Cannot be simplified further (addition and different exponents) |
| ax + ax = a2x ? 2x + 2x = 22x ? |
ax + ax = 2ax 2x + 2x = 2(2x) = 2x+1 |
| a × ax = a2x ? 5 × 5z = 25z ? |
a × ax = ax+1 5 × 5z = 5z+1 |
| −x2 = x2 ? −42 = 16 ? |
−x2 cannot be simplified further −42 = −16 Compare: (−x)2 = x2 and (−4)2 = 16 |
| a × bx = (a × b)x ? 2 × 34 = (2 × 3)4 ? |
Cannot be simplified further |