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

The solution to expand (3a+5b)^3 is 27a^3+135a^2b+225ab^2+125b^3

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expand (3a+5b)^3

expand

(3 a + 5 b)^{3}

27 a^{3} + 135 a^{2} b + 225 a b^{2} + 125 b^{3}

Solution steps

(3 a + 5 b)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 a)^{3} + 3 (3 a)^{2} \cdot 5 b + 3 \cdot 3 a (5 b)^{2} + (5 b)^{3} : 27 a^{3} + 135 a^{2} b + 225 a b^{2} + 125 b^{3}

= 27 a^{3} + 135 a^{2} b + 225 a b^{2} + 125 b^{3}

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x^{4} - 7 x^{2} + 1

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What is expand (3a+5b)^3 ?
The solution to expand (3a+5b)^3 is 27a^3+135a^2b+225ab^2+125b^3