What is expand (4x+1)^4 ?

The solution to expand (4x+1)^4 is 256x^4+256x^3+96x^2+16x+1

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expand (4x+1)^4

expand

(4 x + 1)^{4}

256 x^{4} + 256 x^{3} + 96 x^{2} + 16 x + 1

Solution steps

(4 x + 1)^{4}

Apply binomial theorem:

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

a = 4 x, b = 1

= i = 0 \sum 4 (i 4) (4 x)^{(4 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 x)^{4} \cdot 1^{0} : 256 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 x)^{3} \cdot 1^{1} : 256 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 x)^{2} \cdot 1^{2} : 96 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 x)^{1} \cdot 1^{3} : 16 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 x)^{0} \cdot 1^{4} : 1

= 256 x^{4} + 256 x^{3} + 96 x^{2} + 16 x + 1

\frac{( 3 ^{3} ) ^{2}}{3 ^{5}}

(- 3 x)^{- 1}

- ∣ - 9 ∣

18 n^{3} - 24 n - 21

- 36 \div 6

What is expand (4x+1)^4 ?
The solution to expand (4x+1)^4 is 256x^4+256x^3+96x^2+16x+1