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The binomial theorem provides a way to expand expressions raised to a power in the form of (a+b)ⁿ. It gives a formula for expressing the expanded result as a sum of terms involving coefficients, powers of a and b, and the binomial coefficients. These coefficients can be found using Pascal’s triangle or by calculating combinations. The binomial theorem is widely used in algebra, calculus, and probability theory, making it a powerful tool for simplifying and calculating polynomial expressions efficiently.

The structure of an atom consists of a dense central nucleus, which contains protons and neutrons, surrounded by a cloud of electrons that orbit the nucleus in specific energy levels. The protons have a positive charge, neutrons are neutral, and electrons carry a negative charge. The arrangement of these particles determines the atom’s chemical properties and its interactions with other atoms. The model of the atom has evolved over time, with discoveries by scientists like Rutherford and Bohr contributing to our current understanding of atomic structure.

The cell cycle is the series of events that cells go through as they grow and divide. It consists of interphase, where the cell grows and replicates its DNA, and the mitotic (M) phase, where the cell divides into two daughter cells. The cell cycle is divided into four main stages: G1 (cell growth), S (DNA synthesis), G2 (preparation for division), and M (mitosis or meiosis). Mitosis results in two identical daughter cells, while meiosis leads to the production of gametes with half the original number of chromosomes. Cell division is essential for growth, repair, and reproduction in living organisms.