Solve 4-9(n+k)(n+k-1)

$$4 - 9 ( n + k ) ( n + k - 1 )$$

Evaluate

$$-9\left(n+k\right)\left(n+k-1\right)+4$$

Solution Steps

Multiply -1 and 9 to get -9.

$$4-9\left(n+k\right)\left(n+k-1\right)$$

Use the distributive property to multiply -9 by n+k.

$$4+\left(-9n-9k\right)\left(n+k-1\right)$$

Apply the distributive property by multiplying each term of -9n-9k by each term of n+k-1.

$$4-9n^{2}-9nk+9n-9kn-9k^{2}+9k$$

Combine -9nk and -9kn to get -18nk.

$$4-9n^{2}-18nk+9n-9k^{2}+9k$$

Expand

$$4+9k-9k^{2}+9n-18kn-9n^{2}$$

Solution Steps

Multiply -1 and 9 to get -9.

$$4-9\left(n+k\right)\left(n+k-1\right)$$

Use the distributive property to multiply -9 by n+k.

$$4+\left(-9n-9k\right)\left(n+k-1\right)$$

Apply the distributive property by multiplying each term of -9n-9k by each term of n+k-1.

$$4-9n^{2}-9nk+9n-9kn-9k^{2}+9k$$

Combine -9nk and -9kn to get -18nk.

$$4-9n^{2}-18nk+9n-9k^{2}+9k$$