What is expand (5x^2+1)^3 ?

The solution to expand (5x^2+1)^3 is 125x^6+75x^4+15x^2+1

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expand (5x^2+1)^3

expand

(5 x^{2} + 1)^{3}

125 x^{6} + 75 x^{4} + 15 x^{2} + 1

Solution steps

(5 x^{2} + 1)^{3}

Apply Perfect Cube Formula:

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

(5 x^{2} + 1)^{3} = (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 1 + 3 \cdot 5 x^{2} \cdot 1^{2} + 1^{3}

= (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 1 + 3 \cdot 5 x^{2} \cdot 1^{2} + 1^{3}

Simplify

(5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 1 + 3 \cdot 5 x^{2} \cdot 1^{2} + 1^{3} : 125 x^{6} + 75 x^{4} + 15 x^{2} + 1

= 125 x^{6} + 75 x^{4} + 15 x^{2} + 1

[10 - x]^{2}

(y - 1) (4 y^{2} - 3 y + 1)

5 a^{2} x - 5 a^{2} m - 10 a^{2}

3 a^{2} b - 12 b

(x + y - 1)^{2} - (x - y + 1)^{2}

What is expand (5x^2+1)^3 ?
The solution to expand (5x^2+1)^3 is 125x^6+75x^4+15x^2+1