What is expand (x^2+4)^4 ?

The solution to expand (x^2+4)^4 is x^8+16x^6+96x^4+256x^2+256

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expand (x^2+4)^4

expand

(x^{2} + 4)^{4}

x^{8} + 16 x^{6} + 96 x^{4} + 256 x^{2} + 256

Solution steps

(x^{2} + 4)^{4}

Apply binomial theorem:

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

a = x^{2}, b = 4

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} \cdot 4^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} \cdot 4^{0} : x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} \cdot 4^{1} : 16 x^{6}

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} \cdot 4^{3} : 256 x^{2}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} \cdot 4^{4} : 256

= x^{8} + 16 x^{6} + 96 x^{4} + 256 x^{2} + 256

ln (x^{8})

(x + 2) (x - 1) (x - 2)

(8 x - 9)^{2}

sin (t) - (cos (t) + sin (t))

2 \times 12

What is expand (x^2+4)^4 ?
The solution to expand (x^2+4)^4 is x^8+16x^6+96x^4+256x^2+256