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Popular >

expand (t+3)^4

Solution

expand

(t + 3)^{4}

Solution

t^{4} + 12 t^{3} + 54 t^{2} + 108 t + 81

Solution steps

(t + 3)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = t, b = 3

= i = 0 \sum 4 (i 4) t^{(4 - i)} \cdot 3^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} t^{4} \cdot 3^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} t^{3} \cdot 3^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} t^{2} \cdot 3^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} t^{1} \cdot 3^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} t^{0} \cdot 3^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} t^{4} \cdot 3^{0} : t^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} t^{3} \cdot 3^{1} : 12 t^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} t^{2} \cdot 3^{2} : 54 t^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} t^{1} \cdot 3^{3} : 108 t

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} t^{0} \cdot 3^{4} : 81

= t^{4} + 12 t^{3} + 54 t^{2} + 108 t + 81

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Frequently Asked Questions (FAQ)

What is expand (t+3)^4 ?
The solution to expand (t+3)^4 is t^4+12t^3+54t^2+108t+81