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

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

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expand (2x+y)^4

expand

(2 x + y)^{4}

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

Solution steps

(2 x + y)^{4}

Apply binomial theorem:

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

a = 2 x, b = y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(3 + z)^{5}

(6 - 8 i) 2

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

w^{2} + 8 w + 12

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