What is expand (5x+2y)^4 ?

The solution to expand (5x+2y)^4 is 625x^4+1000x^3y+600x^2y^2+160xy^3+16y^4

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expand (5x+2y)^4

expand

(5 x + 2 y)^{4}

625 x^{4} + 1000 x^{3} y + 600 x^{2} y^{2} + 160 x y^{3} + 16 y^{4}

Solution steps

(5 x + 2 y)^{4}

Apply binomial theorem:

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

a = 5 x, b = 2 y

= i = 0 \sum 4 (i 4) (5 x)^{(4 - i)} (2 y)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x)^{4} (2 y)^{0} : 625 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x)^{3} (2 y)^{1} : 1000 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x)^{2} (2 y)^{2} : 600 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x)^{1} (2 y)^{3} : 160 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x)^{0} (2 y)^{4} : 16 y^{4}

= 625 x^{4} + 1000 x^{3} y + 600 x^{2} y^{2} + 160 x y^{3} + 16 y^{4}

(1 + cot^{2} (x)) cos^{2} (x)

2 0^{6} \cdot (0.5)^{6}

(z - 5) (z + 3)

6 \cdot 6

\frac{45}{( - 9 )}

What is expand (5x+2y)^4 ?
The solution to expand (5x+2y)^4 is 625x^4+1000x^3y+600x^2y^2+160xy^3+16y^4