# How do you expand (t+2)^6?

Jun 2, 2017

$\therefore {\left(t + 2\right)}^{6} = {t}^{6} + 12 {t}^{5} + 60 {t}^{4} + 160 {t}^{3} + 240 {t}^{2} + 192 t + 64$

#### Explanation:

We know ${\left(a + b\right)}^{n} = n {C}_{0} {a}^{n} \cdot {b}^{0} + n {C}_{1} {a}^{n - 1} \cdot {b}^{1} + n {C}_{2} {a}^{n - 2} \cdot {b}^{2} + \ldots \ldots \ldots . + n {C}_{n} {a}^{n - n} \cdot {b}^{n}$

Here $a = t , b = 2 , n = 6$ We know, nC_r = (n!)/(r!*(n-r)!
$\therefore 6 {C}_{0} = 1 , 6 {C}_{1} = 6 , 6 {C}_{2} = 15 , 6 {C}_{3} = 20 , 6 {C}_{4} = 15 , 6 {C}_{5} = 6 , 6 {C}_{6} = 1$

$\therefore {\left(t + 2\right)}^{6} = {t}^{6} + 6 \cdot {t}^{5} \cdot 2 + 15 \cdot {t}^{4} \cdot {2}^{2} + 20 \cdot {t}^{3} \cdot {2}^{3} + 15 \cdot {t}^{2} \cdot {2}^{4} + 6 \cdot t \cdot {2}^{5} + {2}^{6}$ or

$\therefore {\left(t + 2\right)}^{6} = {t}^{6} + 12 \cdot {t}^{5} + 60 \cdot {t}^{4} + 160 \cdot {t}^{3} + 240 \cdot {t}^{2} + 192 \cdot t + 64$ or

$\therefore {\left(t + 2\right)}^{6} = {t}^{6} + 12 {t}^{5} + 60 {t}^{4} + 160 {t}^{3} + 240 {t}^{2} + 192 t + 64$ [Ans]