What is (x+3)^3-(x-1)^3 ?

The solution to (x+3)^3-(x-1)^3 is 12x^2+24x+28

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simplify (x+3)^3-(x-1)^3

simplify

(x + 3)^{3} - (x - 1)^{3}

12 x^{2} + 24 x + 28

Solution steps

(x + 3)^{3} - (x - 1)^{3}

Expand

(x + 3)^{3} : x^{3} + 9 x^{2} + 27 x + 27

= x^{3} + 9 x^{2} + 27 x + 27 - (x - 1)^{3}

Expand

- (x - 1)^{3} : - x^{3} + 3 x^{2} - 3 x + 1

= x^{3} + 9 x^{2} + 27 x + 27 - x^{3} + 3 x^{2} - 3 x + 1

Group like terms

= x^{3} - x^{3} + 9 x^{2} + 3 x^{2} + 27 x - 3 x + 27 + 1

Add similar elements:

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

= 9 x^{2} + 3 x^{2} + 27 x - 3 x + 27 + 1

Add similar elements:

9 x^{2} + 3 x^{2} = 12 x^{2}

= 12 x^{2} + 27 x - 3 x + 27 + 1

Add similar elements:

27 x - 3 x = 24 x

= 12 x^{2} + 24 x + 27 + 1

Add the numbers:

27 + 1 = 28

= 12 x^{2} + 24 x + 28

- 4 x + (- 6) x

(x - 3 x)^{2} - a (x^{2} - 3 x) - 20

\frac{( ( x ^{6} \cdot y ^{8} ) ^{3} )}{( x ^{2} \cdot y ^{2} )}

\frac{8 x}{2}

- 8 (- 6 n + 5) - 4 (8 + 3 n)