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

The solution to (k+1)^3-(k+1) is k^3+3k^2+2k

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

simplify

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

k^{3} + 3 k^{2} + 2 k

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

- (k + 1) = - k - 1

= (k + 1)^{3} - k - 1

Expand

(k + 1)^{3} : k^{3} + 3 k^{2} + 3 k + 1

= k^{3} + 3 k^{2} + 3 k + 1 - k - 1

Group like terms

= k^{3} + 3 k^{2} + 3 k - k + 1 - 1

Add similar elements:

3 k - k = 2 k

= k^{3} + 3 k^{2} + 2 k + 1 - 1

Subtract the numbers:

1 - 1 = 0

= k^{3} + 3 k^{2} + 2 k

(2 x + 5)^{4}

\frac{x}{2} + \frac{x}{4}

(- 7)^{5}

(t - 2)^{4}

\frac{8 x + 64}{x - 4} \cdot \frac{x ^{2} - 49}{x ^{2} + x - 56}