Solve xleft(3n+4right)-left(n-1right)left(3n+1right)

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

The opposite of -2n is 2n.

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

The opposite of -1 is 1.

$$3xn+4x-3n^{2}+2n+1$$

Expand

$$3nx+4x-3n^{2}+2n+1$$

Solution Steps

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

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

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

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

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

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

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

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

The opposite of -2n is 2n.

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

The opposite of -1 is 1.

$$3xn+4x-3n^{2}+2n+1$$