What is expand (5x+y)^4 ?

The solution to expand (5x+y)^4 is 625x^4+500x^3y+150x^2y^2+20xy^3+y^4

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expand (5x+y)^4

expand

(5 x + y)^{4}

625 x^{4} + 500 x^{3} y + 150 x^{2} y^{2} + 20 x y^{3} + y^{4}

Solution steps

(5 x + y)^{4}

Apply binomial theorem:

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

a = 5 x, b = y

= i = 0 \sum 4 (i 4) (5 x)^{(4 - i)} y^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x)^{4} y^{0} : 625 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x)^{3} y^{1} : 500 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x)^{2} y^{2} : 150 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x)^{1} y^{3} : 20 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x)^{0} y^{4} : y^{4}

= 625 x^{4} + 500 x^{3} y + 150 x^{2} y^{2} + 20 x y^{3} + y^{4}

\frac{x - 2 x}{x + 2 x}

x y + 2 x + y + 2

x + 19 x + 21

2^{2} - x^{2}

6 x + 42

What is expand (5x+y)^4 ?
The solution to expand (5x+y)^4 is 625x^4+500x^3y+150x^2y^2+20xy^3+y^4