What is expand (t+h)^4 ?

The solution to expand (t+h)^4 is t^4+4t^3h+6t^2h^2+4th^3+h^4

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expand (t+h)^4

expand

(t + h)^{4}

t^{4} + 4 t^{3} h + 6 t^{2} h^{2} + 4 t h^{3} + h^{4}

Solution steps

(t + h)^{4}

Apply binomial theorem:

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

a = t, b = h

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} t^{2} h^{2} : 6 t^{2} h^{2}

Simplify

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

Simplify

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

= t^{4} + 4 t^{3} h + 6 t^{2} h^{2} + 4 t h^{3} + h^{4}

2023 \cdot 4.57 + 202.3 \cdot 5.43

\frac{( 2 x ^{2} + 5 x - 7 )}{( 10 x + 35 )}

\frac{( y ^{3} - y ^{2} + y - 1 )}{( y ^{3} + y ^{2} + y + 1 )}

(\frac{5}{x}) + 2 (y - 1)

x y + x y^{2}

What is expand (t+h)^4 ?
The solution to expand (t+h)^4 is t^4+4t^3h+6t^2h^2+4th^3+h^4