Solve h(3n+4)-(n-1)(3n+1)

$$h ( 3 n + 4 ) - ( n - 1 ) ( 3 n + 1 )$$

Evaluate

$$-\left(n-1\right)\left(3n+1\right)+h\left(3n+4\right)$$

Solution Steps

Use the distributive property to multiply h by 3n+4.

$$3hn+4h-\left(n-1\right)\left(3n+1\right)$$

Apply the distributive property by multiplying each term of n-1 by each term of 3n+1.

$$3hn+4h-\left(3n^{2}+n-3n-1\right)$$

Combine n and -3n to get -2n.

$$3hn+4h-\left(3n^{2}-2n-1\right)$$

To find the opposite of 3n^{2}-2n-1, find the opposite of each term.

$$3hn+4h-3n^{2}-\left(-2n\right)-\left(-1\right)$$

The opposite of -2n is 2n.

$$3hn+4h-3n^{2}+2n-\left(-1\right)$$

The opposite of -1 is 1.

$$3hn+4h-3n^{2}+2n+1$$

Expand

$$1+4h+2n+3hn-3n^{2}$$

Solution Steps

Use the distributive property to multiply h by 3n+4.

$$3hn+4h-\left(n-1\right)\left(3n+1\right)$$

Apply the distributive property by multiplying each term of n-1 by each term of 3n+1.

$$3hn+4h-\left(3n^{2}+n-3n-1\right)$$

Combine n and -3n to get -2n.

$$3hn+4h-\left(3n^{2}-2n-1\right)$$

To find the opposite of 3n^{2}-2n-1, find the opposite of each term.

$$3hn+4h-3n^{2}-\left(-2n\right)-\left(-1\right)$$

The opposite of -2n is 2n.

$$3hn+4h-3n^{2}+2n-\left(-1\right)$$

The opposite of -1 is 1.

$$3hn+4h-3n^{2}+2n+1$$