Solve =(3x+7)(2x^2)+(3x+7)(-5x)+(3x+7)6

$$= ( 3 x + 7 ) ( 2 x ^ { 2 } ) + ( 3 x + 7 ) ( - 5 x ) + ( 3 x + 7 ) 6$$

Evaluate

$$\left(3x+7\right)\left(2x^{2}-5x+6\right)$$

Solution Steps

Use the distributive property to multiply 3x+7 by 2.

$$\left(6x+14\right)x^{2}+\left(3x+7\right)\left(-5\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 6x+14 by x^{2}.

$$6x^{3}+14x^{2}+\left(3x+7\right)\left(-5\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by -5.

$$6x^{3}+14x^{2}+\left(-15x-35\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply -15x-35 by x.

$$6x^{3}+14x^{2}-15x^{2}-35x+\left(3x+7\right)\times 6$$

Combine 14x^{2} and -15x^{2} to get -x^{2}.

$$6x^{3}-x^{2}-35x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by 6.

$$6x^{3}-x^{2}-35x+18x+42$$

Combine -35x and 18x to get -17x.

$$6x^{3}-x^{2}-17x+42$$

Expand

$$6x^{3}-x^{2}-17x+42$$

Solution Steps

Use the distributive property to multiply 3x+7 by 2.

$$\left(6x+14\right)x^{2}+\left(3x+7\right)\left(-5\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 6x+14 by x^{2}.

$$6x^{3}+14x^{2}+\left(3x+7\right)\left(-5\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by -5.

$$6x^{3}+14x^{2}+\left(-15x-35\right)x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply -15x-35 by x.

$$6x^{3}+14x^{2}-15x^{2}-35x+\left(3x+7\right)\times 6$$

Combine 14x^{2} and -15x^{2} to get -x^{2}.

$$6x^{3}-x^{2}-35x+\left(3x+7\right)\times 6$$

Use the distributive property to multiply 3x+7 by 6.

$$6x^{3}-x^{2}-35x+18x+42$$

Combine -35x and 18x to get -17x.

$$6x^{3}-x^{2}-17x+42$$