1. **Problem statement:** Simplify the expression or expand the power without using the binomial theorem. 2. **General approach:** Normally, the binomial theorem is used to expand expressions like $ (a+b)^n $. Since we cannot use it, we will use repeated multiplication. 3. **Example:** Suppose the problem is to expand $ (x+2)^3 $ without the binomial theorem. 4. **Step-by-step expansion:** $$ (x+2)^3 = (x+2)(x+2)(x+2) $$ First, multiply the first two factors: $$ (x+2)(x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4 $$ 5. Now multiply this result by the third factor $(x+2)$: $$ (x^2 + 4x + 4)(x+2) = x^2(x+2) + 4x(x+2) + 4(x+2) $$ 6. Distribute each term: $$ = x^3 + 2x^2 + 4x^2 + 8x + 4x + 8 $$ 7. Combine like terms: $$ = x^3 + (2x^2 + 4x^2) + (8x + 4x) + 8 = x^3 + 6x^2 + 12x + 8 $$ 8. **Final answer:** $$ (x+2)^3 = x^3 + 6x^2 + 12x + 8 $$ This method can be used for any power by repeated multiplication.