What is expand (3x+5y)^4 ?

The solution to expand (3x+5y)^4 is 81x^4+540x^3y+1350x^2y^2+1500xy^3+625y^4

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expand (3x+5y)^4

expand

(3 x + 5 y)^{4}

81 x^{4} + 540 x^{3} y + 1350 x^{2} y^{2} + 1500 x y^{3} + 625 y^{4}

Solution steps

(3 x + 5 y)^{4}

Apply binomial theorem:

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

a = 3 x, b = 5 y

= i = 0 \sum 4 (i 4) (3 x)^{(4 - i)} (5 y)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (5 y)^{0} : 81 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (5 y)^{1} : 540 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (5 y)^{2} : 1350 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (5 y)^{3} : 1500 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (5 y)^{4} : 625 y^{4}

= 81 x^{4} + 540 x^{3} y + 1350 x^{2} y^{2} + 1500 x y^{3} + 625 y^{4}

4 x^{3} - 4 x^{2} - 21 x - 9

(2 p + q) (p - 2 q + 3 r) - (p - 3 q) (- 3 p + q - 2 r)

\frac{lo g _{a^{2}} ( b )}{( lo g _{a} ( b ^{2} ) )}

2 lo g_{10} (x^{5})

\frac{\frac{143}{2}}{x} - \frac{1}{4} - \frac{1}{12}

What is expand (3x+5y)^4 ?
The solution to expand (3x+5y)^4 is 81x^4+540x^3y+1350x^2y^2+1500xy^3+625y^4