What is expand (2y+3x)^5 ?

The solution to expand (2y+3x)^5 is 32y^5+240y^4x+720y^3x^2+1080y^2x^3+810yx^4+243x^5

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expand (2y+3x)^5

expand

(2 y + 3 x)^{5}

32 y^{5} + 240 y^{4} x + 720 y^{3} x^{2} + 1080 y^{2} x^{3} + 810 y x^{4} + 243 x^{5}

Solution steps

(2 y + 3 x)^{5}

Apply binomial theorem:

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

a = 2 y, b = 3 x

= i = 0 \sum 5 (i 5) (2 y)^{(5 - i)} (3 x)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 y)^{5} (3 x)^{0} : 32 y^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 y)^{4} (3 x)^{1} : 240 y^{4} x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 y)^{3} (3 x)^{2} : 720 y^{3} x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 y)^{2} (3 x)^{3} : 1080 y^{2} x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 y)^{1} (3 x)^{4} : 810 y x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 y)^{0} (3 x)^{5} : 243 x^{5}

= 32 y^{5} + 240 y^{4} x + 720 y^{3} x^{2} + 1080 y^{2} x^{3} + 810 y x^{4} + 243 x^{5}

5^{x + 2} + 5^{x + 1}

107 + 428 - 663

(2 a^{3} + 5 b^{4})^{3}

43 \times 23

- \frac{1}{2} lo g_{5} (25)

What is expand (2y+3x)^5 ?
The solution to expand (2y+3x)^5 is 32y^5+240y^4x+720y^3x^2+1080y^2x^3+810yx^4+243x^5