Subjects algebra

Factorization Grouping

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1. **Stating the problem:** We need to factorize the given algebraic expression by grouping like terms. 2. **Understanding factorization by grouping:** This method involves grouping terms with common factors and factoring each group separately, then factoring out the common binomial factor. 3. **Given expression:** The user input is unclear, but let's assume a general example similar to the pattern: $$123x + 176t + 123x + 244 + 11bx + 99 + 91 + 1117 + 2634 + 146^2 - 305cd$$ 4. **Group like terms:** Group terms with common variables or constants: $$ (123x + 123x + 11bx) + (176t) + (244 + 99 + 91 + 1117 + 2634) + (146^2) - 305cd $$ 5. **Simplify each group:** - Combine like terms in the first group: $$123x + 123x = 246x$$, so first group becomes $$246x + 11bx$$. - The second group is $$176t$$. - Sum constants in the third group: $$244 + 99 + 91 + 1117 + 2634 = 4185$$. - The fourth term is $$146^2 = 21316$$. - The last term is $$-305cd$$. 6. **Factor common terms in the first group:** $$246x + 11bx = x(246 + 11b)$$ 7. **Rewrite the expression:** $$x(246 + 11b) + 176t + 4185 + 21316 - 305cd$$ 8. **Conclusion:** Without clearer grouping or more structure, further factorization is limited. The main factorization by grouping is in the first group. **Final answer:** $$x(246 + 11b) + 176t + 4185 + 21316 - 305cd$$