What is (2x+5)^3-(2x-5)^3 ?

The solution to (2x+5)^3-(2x-5)^3 is 120x^2+250

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simplify (2x+5)^3-(2x-5)^3

simplify

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

120 x^{2} + 250

Solution steps

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

Expand

(2 x + 5)^{3} : 8 x^{3} + 60 x^{2} + 150 x + 125

= 8 x^{3} + 60 x^{2} + 150 x + 125 - (2 x - 5)^{3}

Expand

- (2 x - 5)^{3} : - 8 x^{3} + 60 x^{2} - 150 x + 125

= 8 x^{3} + 60 x^{2} + 150 x + 125 - 8 x^{3} + 60 x^{2} - 150 x + 125

Group like terms

= 8 x^{3} - 8 x^{3} + 60 x^{2} + 60 x^{2} + 150 x - 150 x + 125 + 125

Add similar elements:

8 x^{3} - 8 x^{3} = 0

= 60 x^{2} + 60 x^{2} + 150 x - 150 x + 125 + 125

Add similar elements:

60 x^{2} + 60 x^{2} = 120 x^{2}

= 120 x^{2} + 150 x - 150 x + 125 + 125

Add similar elements:

150 x - 150 x = 0

= 120 x^{2} + 125 + 125

Add the numbers:

125 + 125 = 250

= 120 x^{2} + 250

(\frac{f}{g}) (1)

25 x^{12} + 25 x^{6} \cdot y + 25 y^{2}

\frac{( 3 y ^{2} + 8 y + 4 )}{( y ^{2} - 4 )}

(- 2^{- 1} x^{- n})^{- 3}

\frac{54}{24 - 3 x [ \frac{( 4 \cdot 5 - 2 \cdot 5 )}{2} + 1 ]}