Solve (2x+3)(6x+2)-6x(2x+13)+8(7x+2)

$$( 2 x + 3 ) ( 6 x + 2 ) - 6 x ( 2 x + 13 ) + 8 ( 7 x + 2 )$$

Evaluate

$$22$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+3 by each term of 6x+2.

$$12x^{2}+4x+18x+6-6x\left(2x+13\right)+8\left(7x+2\right)$$

Combine 4x and 18x to get 22x.

$$12x^{2}+22x+6-6x\left(2x+13\right)+8\left(7x+2\right)$$

Use the distributive property to multiply 8 by 7x+2.

$$12x^{2}+22x+6-6x\left(2x+13\right)+56x+16$$

Use the distributive property to multiply -6x by 2x+13.

$$12x^{2}+22x+6-12x^{2}-78x+56x+16$$

Combine 12x^{2} and -12x^{2} to get 0.

$$22x+6-78x+56x+16$$

Combine 22x and -78x to get -56x.

$$-56x+6+56x+16$$

Combine -56x and 56x to get 0.

$$6+16$$

Add 6 and 16 to get 22.

$$22$$

Factor

$$2\times 11$$

Solution Steps

Factor out 2.

$$2\left(\left(2x+3\right)\left(3x+1\right)-3x\left(2x+13\right)+4\left(7x+2\right)\right)$$

Simplify.

$$22$$