What is expand (3x^2+y)^5 ?

The solution to expand (3x^2+y)^5 is 243x^{10}+405x^8y+270x^6y^2+90x^4y^3+15x^2y^4+y^5

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expand (3x^2+y)^5

expand

(3 x^{2} + y)^{5}

243 x^{10} + 405 x^{8} y + 270 x^{6} y^{2} + 90 x^{4} y^{3} + 15 x^{2} y^{4} + y^{5}

Solution steps

(3 x^{2} + y)^{5}

Apply binomial theorem:

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

a = 3 x^{2}, b = y

= i = 0 \sum 5 (i 5) (3 x^{2})^{(5 - i)} y^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x^{2})^{5} y^{0} : 243 x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x^{2})^{4} y^{1} : 405 x^{8} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x^{2})^{3} y^{2} : 270 x^{6} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x^{2})^{2} y^{3} : 90 x^{4} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x^{2})^{1} y^{4} : 15 x^{2} y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x^{2})^{0} y^{5} : y^{5}

= 243 x^{10} + 405 x^{8} y + 270 x^{6} y^{2} + 90 x^{4} y^{3} + 15 x^{2} y^{4} + y^{5}

(2 - 1) 5

x^{1 - 1}

\frac{3}{x - 1} - \frac{2}{x}

(6 t^{2} - 3 t + 5) (7 t - 4)

\frac{\frac{1}{4} + \frac{1}{x}}{4 + x}

What is expand (3x^2+y)^5 ?
The solution to expand (3x^2+y)^5 is 243x^{10}+405x^8y+270x^6y^2+90x^4y^3+15x^2y^4+y^5