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

The solution to expand (5x^2+z)^4 is 625x^8+500x^6z+150x^4z^2+20x^2z^3+z^4

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expand (5x^2+z)^4

expand

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

625 x^{8} + 500 x^{6} z + 150 x^{4} z^{2} + 20 x^{2} z^{3} + z^{4}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{2})^{3} z^{1} : 500 x^{6} z

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{2})^{2} z^{2} : 150 x^{4} z^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{2})^{1} z^{3} : 20 x^{2} z^{3}

Simplify

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

= 625 x^{8} + 500 x^{6} z + 150 x^{4} z^{2} + 20 x^{2} z^{3} + z^{4}

22 - 22

11 \times 8

\frac{- 4 x}{x ^{2}}

\frac{9}{x + 9} - \frac{1}{x}

What is expand (5x^2+z)^4 ?
The solution to expand (5x^2+z)^4 is 625x^8+500x^6z+150x^4z^2+20x^2z^3+z^4