# What is the binomial theorem?

Feb 1, 2016

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#### Explanation:

Binomial theorem is a kind of formula that helps us to expand binomials raised to the power of any number using the pascals triangle or using the binomial theorem.

Watch the video to now about the pascal's triangle and the binomial theorem.

Now we can use the pascal's triangle to solve the following expressions:

${\left(a + b\right)}^{2} = 1 {a}^{2} + 2 a b + 1 {b}^{2} = {a}^{2} + 2 a b + {b}^{2}$

$E g . \left(2 + b\right) = 1 \left({2}^{2}\right) + 2 \left(2 b\right) + 1 \left({b}^{2}\right) = 1 \left(4\right) + 2 \left(2 b\right) + 1 \left({b}^{2}\right) = 4 + 4 b + {b}^{2}$

${\left(a + b\right)}^{3} = 1 {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + 1 {b}^{3}$

$E g . {\left(b + 5\right)}^{3} = 1 {b}^{3} + 3 {b}^{2}$$5 + 3 b {5}^{2} + 1 \left({5}^{3}\right) = {b}^{3} + 15 {b}^{2} + 75 b + 125$