Solve 5(1+3x)(3m-1)+9(1/3m)(m+1/3)

$$5 ( 1 + 3 x ) ( 3 m - 1 ) + 9 ( \frac { 1 } { 3 } m ) ( m + \frac { 1 } { 3 } )$$

Evaluate

$$m\left(3m+1\right)+5\left(3m-1\right)\left(3x+1\right)$$

Solution Steps

Use the distributive property to multiply 5 by 1+3x.

$$\left(5+15x\right)\left(3m-1\right)+9\times \frac{1}{3}m\left(m+\frac{1}{3}\right)$$

Apply the distributive property by multiplying each term of 5+15x by each term of 3m-1.

$$15m-5+45xm-15x+9\times \frac{1}{3}m\left(m+\frac{1}{3}\right)$$

Multiply 9 and \frac{1}{3} to get \frac{9}{3}.

$$15m-5+45xm-15x+\frac{9}{3}m\left(m+\frac{1}{3}\right)$$

Divide 9 by 3 to get 3.

$$15m-5+45xm-15x+3m\left(m+\frac{1}{3}\right)$$

Use the distributive property to multiply 3m by m+\frac{1}{3}.

$$15m-5+45xm-15x+3m^{2}+3m\times \frac{1}{3}$$

Cancel out 3 and 3.

$$15m-5+45xm-15x+3m^{2}+m$$

Combine 15m and m to get 16m.

$$16m-5+45xm-15x+3m^{2}$$

Expand

$$45mx-15x+3m^{2}+16m-5$$

Solution Steps

Use the distributive property to multiply 5 by 1+3x.

$$\left(5+15x\right)\left(3m-1\right)+9\times \frac{1}{3}m\left(m+\frac{1}{3}\right)$$

Apply the distributive property by multiplying each term of 5+15x by each term of 3m-1.

$$15m-5+45xm-15x+9\times \frac{1}{3}m\left(m+\frac{1}{3}\right)$$

Multiply 9 and \frac{1}{3} to get \frac{9}{3}.

$$15m-5+45xm-15x+\frac{9}{3}m\left(m+\frac{1}{3}\right)$$

Divide 9 by 3 to get 3.

$$15m-5+45xm-15x+3m\left(m+\frac{1}{3}\right)$$

Use the distributive property to multiply 3m by m+\frac{1}{3}.

$$15m-5+45xm-15x+3m^{2}+3m\times \frac{1}{3}$$

Cancel out 3 and 3.

$$15m-5+45xm-15x+3m^{2}+m$$

Combine 15m and m to get 16m.

$$16m-5+45xm-15x+3m^{2}$$