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

The solution to expand (y^2+2x)^4 is y^8+8y^6x+24y^4x^2+32y^2x^3+16x^4

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expand (y^2+2x)^4

expand

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

y^{8} + 8 y^{6} x + 24 y^{4} x^{2} + 32 y^{2} x^{3} + 16 x^{4}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (y^{2})^{3} (2 x)^{1} : 8 y^{6} x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (y^{2})^{2} (2 x)^{2} : 24 y^{4} x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (y^{2})^{1} (2 x)^{3} : 32 y^{2} x^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (y^{2})^{0} (2 x)^{4} : 16 x^{4}

= y^{8} + 8 y^{6} x + 24 y^{4} x^{2} + 32 y^{2} x^{3} + 16 x^{4}

\frac{2}{1}

3 x^{3} - 375

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

\frac{2}{5} \div 5

0 + 6

What is expand (y^2+2x)^4 ?
The solution to expand (y^2+2x)^4 is y^8+8y^6x+24y^4x^2+32y^2x^3+16x^4