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

The solution to expand (x+4y)^4 is x^4+16x^3y+96x^2y^2+256xy^3+256y^4

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expand (x+4y)^4

expand

(x + 4 y)^{4}

x^{4} + 16 x^{3} y + 96 x^{2} y^{2} + 256 x y^{3} + 256 y^{4}

Solution steps

(x + 4 y)^{4}

Apply binomial theorem:

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

a = x, b = 4 y

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (4 y)^{1} : 16 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (4 y)^{2} : 96 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (4 y)^{3} : 256 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (4 y)^{4} : 256 y^{4}

= x^{4} + 16 x^{3} y + 96 x^{2} y^{2} + 256 x y^{3} + 256 y^{4}

- \frac{sin ( x )}{cos ( x )}

(a - 4 b) (3 a + 2 b)

(2^{\frac{1}{2}} 221) (3^{\frac{1}{3}} 331) (4^{\frac{1}{6}} 461)

(1 + cot^{2} (x)) (1 - sin^{2} (x))

What is expand (x+4y)^4 ?
The solution to expand (x+4y)^4 is x^4+16x^3y+96x^2y^2+256xy^3+256y^4