What is expand (2a+5b)^3 ?

The solution to expand (2a+5b)^3 is 8a^3+60a^2b+150ab^2+125b^3

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expand (2a+5b)^3

expand

(2 a + 5 b)^{3}

8 a^{3} + 60 a^{2} b + 150 a b^{2} + 125 b^{3}

Solution steps

(2 a + 5 b)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(2 a + 5 b)^{3} = (2 a)^{3} + 3 (2 a)^{2} \cdot 5 b + 3 \cdot 2 a (5 b)^{2} + (5 b)^{3}

= (2 a)^{3} + 3 (2 a)^{2} \cdot 5 b + 3 \cdot 2 a (5 b)^{2} + (5 b)^{3}

Simplify

(2 a)^{3} + 3 (2 a)^{2} \cdot 5 b + 3 \cdot 2 a (5 b)^{2} + (5 b)^{3} : 8 a^{3} + 60 a^{2} b + 150 a b^{2} + 125 b^{3}

= 8 a^{3} + 60 a^{2} b + 150 a b^{2} + 125 b^{3}

\frac{9}{8} \cdot \frac{1}{2}

2 x^{2} - 2 x - 5 x y + 5 y

\frac{1225}{5}

h^{2} - 10 h + 25

\frac{5 ^{4}}{5 ^{7}}

What is expand (2a+5b)^3 ?
The solution to expand (2a+5b)^3 is 8a^3+60a^2b+150ab^2+125b^3