When a binomial expression is raised to a power ‘n’ we need to expand it. The binomial theorem assists us in doing this. It converts such an expression into a series. It shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying out. The solution to the problem of the binomial coefficient without actually multiplying out, is called the binomial theorem. It gives the coefficients for the expansion of (a + b)n.
The Binomial Theorem is a quick way of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression (3x – 2)10 would be very painful to multiply out by hand. This can be done by a simple formula, and we can plug the binomial 3x – 2 and the power 10 into that formula to get that expanded (multiplied-out) form. Binomial Theorem helps us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
The Binomial Theorem is a quick way of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression (3x – 2)10 would be very painful to multiply out by hand. This can be done by a simple formula, and we can plug the binomial 3x – 2 and the power 10 into that formula to get that expanded (multiplied-out) form. Binomial Theorem helps us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
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