What is expand (x^2-z)^4 ?

The solution to expand (x^2-z)^4 is x^8-4x^6z+6x^4z^2-4x^2z^3+z^4

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expand (x^2-z)^4

expand

(x^{2} - z)^{4}

x^{8} - 4 x^{6} z + 6 x^{4} z^{2} - 4 x^{2} z^{3} + z^{4}

Solution steps

(x^{2} - z)^{4}

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (- z)^{2} : 6 x^{4} z^{2}

Simplify

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

Simplify

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

= x^{8} - 4 x^{6} z + 6 x^{4} z^{2} - 4 x^{2} z^{3} + z^{4}

2 x^{2} + 20 x + 42

5 y^{2} + 13 y + 6

\frac{94}{19}

\frac{23}{16}

16 \cdot 5 \frac{7}{8}

What is expand (x^2-z)^4 ?
The solution to expand (x^2-z)^4 is x^8-4x^6z+6x^4z^2-4x^2z^3+z^4