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

The solution to expand (2a^2+4)^4 is 16a^8+128a^6+384a^4+512a^2+256

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expand (2a^2+4)^4

expand

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

16 a^{8} + 128 a^{6} + 384 a^{4} + 512 a^{2} + 256

Solution steps

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

Apply binomial theorem:

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

a = 2 a^{2}, b = 4

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 a^{2})^{4} \cdot 4^{0} : 16 a^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 a^{2})^{3} \cdot 4^{1} : 128 a^{6}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 a^{2})^{2} \cdot 4^{2} : 384 a^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 a^{2})^{1} \cdot 4^{3} : 512 a^{2}

Simplify

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

= 16 a^{8} + 128 a^{6} + 384 a^{4} + 512 a^{2} + 256

\frac{1}{25} a^{2} b^{2} - 25

- 4.5 y - 8.2

(x - 1) - (x^{2} - 1)

a^{2} x^{4} + a^{3} x^{2} - 5 a^{4} x

p (x) 4 x^{3} - 12 x^{2} + 11 x - 5

What is expand (2a^2+4)^4 ?
The solution to expand (2a^2+4)^4 is 16a^8+128a^6+384a^4+512a^2+256