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

The solution to (5a+2)^3-(5a-2)^3 is 300a^2+16

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

simplify

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

300 a^{2} + 16

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

125 a^{3} - 125 a^{3} = 0

= 150 a^{2} + 150 a^{2} + 60 a - 60 a + 8 + 8

Add similar elements:

150 a^{2} + 150 a^{2} = 300 a^{2}

= 300 a^{2} + 60 a - 60 a + 8 + 8

Add similar elements:

60 a - 60 a = 0

= 300 a^{2} + 8 + 8

Add the numbers:

8 + 8 = 16

= 300 a^{2} + 16

\frac{( y ^{2} + 7 y + 10 )}{( y + 5 )}

\frac{81}{49 \cdot x ^{4} \cdot y ^{10}}

\frac{( 12 x ^{8} \cdot y ^{3} )}{( - 3 x ^{2} \cdot y )}

(b cos (a))^{2} + (b sin (a))^{2}

a^{5} - a^{3} \cdot b^{2} - a^{2} \cdot b^{3} + b^{5}