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

The solution to expand (3x+4y)^5 is 243x^5+1620x^4y+4320x^3y^2+5760x^2y^3+3840xy^4+1024y^5

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expand (3x+4y)^5

expand

(3 x + 4 y)^{5}

243 x^{5} + 1620 x^{4} y + 4320 x^{3} y^{2} + 5760 x^{2} y^{3} + 3840 x y^{4} + 1024 y^{5}

Solution steps

(3 x + 4 y)^{5}

Apply binomial theorem:

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

a = 3 x, b = 4 y

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (4 y)^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (4 y)^{1} : 1620 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (4 y)^{2} : 4320 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (4 y)^{3} : 5760 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (4 y)^{4} : 3840 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (4 y)^{5} : 1024 y^{5}

= 243 x^{5} + 1620 x^{4} y + 4320 x^{3} y^{2} + 5760 x^{2} y^{3} + 3840 x y^{4} + 1024 y^{5}

\frac{( 12 a ^{3} b ^{2} + 10 a ^{2} b ^{3} )}{2 ab}

\frac{45}{6}

\frac{5 x - 25}{x ^{2} - 7 x + 10}

\frac{\frac{1}{s}}{1 + \frac{1}{s}}

(3 - 2 i) - (- 4 + i)

What is expand (3x+4y)^5 ?
The solution to expand (3x+4y)^5 is 243x^5+1620x^4y+4320x^3y^2+5760x^2y^3+3840xy^4+1024y^5