What is expand (5x^2+4)^4 ?

The solution to expand (5x^2+4)^4 is 625x^8+2000x^6+2400x^4+1280x^2+256

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expand (5x^2+4)^4

expand

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

625 x^{8} + 2000 x^{6} + 2400 x^{4} + 1280 x^{2} + 256

Solution steps

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

Apply binomial theorem:

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

a = 5 x^{2}, b = 4

= i = 0 \sum 4 (i 4) (5 x^{2})^{(4 - i)} \cdot 4^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (5 x^{2})^{4} \cdot 4^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{2})^{3} \cdot 4^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{2})^{2} \cdot 4^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{2})^{1} \cdot 4^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (5 x^{2})^{0} \cdot 4^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x^{2})^{4} \cdot 4^{0} : 625 x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{2})^{3} \cdot 4^{1} : 2000 x^{6}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{2})^{2} \cdot 4^{2} : 2400 x^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{2})^{1} \cdot 4^{3} : 1280 x^{2}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x^{2})^{0} \cdot 4^{4} : 256

= 625 x^{8} + 2000 x^{6} + 2400 x^{4} + 1280 x^{2} + 256

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8 x + 20

(cos (2 x)) (cos (2 x))

4 x^{2} y

What is expand (5x^2+4)^4 ?
The solution to expand (5x^2+4)^4 is 625x^8+2000x^6+2400x^4+1280x^2+256