What is expand (2z^2-y)^5 ?

The solution to expand (2z^2-y)^5 is 32z^{10}-80z^8y+80z^6y^2-40z^4y^3+10z^2y^4-y^5

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expand (2z^2-y)^5

expand

(2 z^{2} - y)^{5}

32 z^{10} - 80 z^{8} y + 80 z^{6} y^{2} - 40 z^{4} y^{3} + 10 z^{2} y^{4} - y^{5}

Solution steps

(2 z^{2} - y)^{5}

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 z^{2})^{5} (- y)^{0} : 32 z^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 z^{2})^{4} (- y)^{1} : - 80 z^{8} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 z^{2})^{3} (- y)^{2} : 80 z^{6} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 z^{2})^{2} (- y)^{3} : - 40 z^{4} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 z^{2})^{1} (- y)^{4} : 10 z^{2} y^{4}

Simplify

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

= 32 z^{10} - 80 z^{8} y + 80 z^{6} y^{2} - 40 z^{4} y^{3} + 10 z^{2} y^{4} - y^{5}

3 \times \frac{3}{8}

\frac{3 x ^{2}}{8} \cdot \frac{24}{x ^{3}}

x^{5} y^{2} - y^{4}

\frac{2}{6} - 1

\frac{4}{52} \times \frac{4}{52}

What is expand (2z^2-y)^5 ?
The solution to expand (2z^2-y)^5 is 32z^{10}-80z^8y+80z^6y^2-40z^4y^3+10z^2y^4-y^5