What is expand (x+y)^4 ?

The solution to expand (x+y)^4 is x^4+4x^3y+6x^2y^2+4xy^3+y^4

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expand (x+y)^4

expand

(x + y)^{4}

x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4 x y^{3} + y^{4}

Solution steps

(x + y)^{4}

Apply binomial theorem:

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

a = x, b = y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= x^{4} + 4 x^{3} y + 6 x^{2} y^{2} + 4 x y^{3} + y^{4}

\frac{5 m ^{2} - 15 m}{m - 3}

2 n^{3} + 3 n^{2} + n

\frac{x - 3}{5} - 1 = \frac{x - 5}{4}

\frac{300}{5}

∣ 2 x - 3 ∣ = - 2

What is expand (x+y)^4 ?
The solution to expand (x+y)^4 is x^4+4x^3y+6x^2y^2+4xy^3+y^4