What is expand (3m^2+5n^2)^3 ?

The solution to expand (3m^2+5n^2)^3 is 27m^6+135m^4n^2+225m^2n^4+125n^6

Popular >

expand (3m^2+5n^2)^3

expand

(3 m^{2} + 5 n^{2})^{3}

27 m^{6} + 135 m^{4} n^{2} + 225 m^{2} n^{4} + 125 n^{6}

Solution steps

(3 m^{2} + 5 n^{2})^{3}

Apply Perfect Cube Formula:

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

(3 m^{2} + 5 n^{2})^{3} = (3 m^{2})^{3} + 3 (3 m^{2})^{2} \cdot 5 n^{2} + 3 \cdot 3 m^{2} (5 n^{2})^{2} + (5 n^{2})^{3}

= (3 m^{2})^{3} + 3 (3 m^{2})^{2} \cdot 5 n^{2} + 3 \cdot 3 m^{2} (5 n^{2})^{2} + (5 n^{2})^{3}

Simplify

(3 m^{2})^{3} + 3 (3 m^{2})^{2} \cdot 5 n^{2} + 3 \cdot 3 m^{2} (5 n^{2})^{2} + (5 n^{2})^{3} : 27 m^{6} + 135 m^{4} n^{2} + 225 m^{2} n^{4} + 125 n^{6}

= 27 m^{6} + 135 m^{4} n^{2} + 225 m^{2} n^{4} + 125 n^{6}

a^{3} - 27 b^{3}

(x - 1) (x - 2) - (x - 3) (x - 4) + (x + 5) (x + 6)

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

(\frac{x}{3 + 1})^{2}

(\frac{x + 1}{x - 1})^{2}

What is expand (3m^2+5n^2)^3 ?
The solution to expand (3m^2+5n^2)^3 is 27m^6+135m^4n^2+225m^2n^4+125n^6