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

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

Expand

$$1+2k-2k^{3}-k^{4}$$

Solution Steps

To find the opposite of k-1, find the opposite of each term.

$$\left(-k+1\right)\left(k+1\right)^{3}$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(k+1\right)^{3}.

$$\left(-k+1\right)\left(k^{3}+3k^{2}+3k+1\right)$$

Use the distributive property to multiply -k+1 by k^{3}+3k^{2}+3k+1 and combine like terms.

$$-k^{4}-2k^{3}+2k+1$$

Evaluate

$$-\left(k-1\right)\left(k+1\right)^{3}$$

Solution Steps

To find the opposite of k-1, find the opposite of each term.

$$\left(-k+1\right)\left(k+1\right)^{3}$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(k+1\right)^{3}.

$$\left(-k+1\right)\left(k^{3}+3k^{2}+3k+1\right)$$

Use the distributive property to multiply -k+1 by k^{3}+3k^{2}+3k+1 and combine like terms.

$$-k^{4}-2k^{3}+2k+1$$