Solve 3(4x-5)(2x+3)-1+(x+2)(2x+3)

$$3(4x-5)(2x+3)-1+(x+2)(2x+3)$$

Evaluate

$$26x^{2}+13x-40$$

Solution Steps

Use the distributive property to multiply 3 by 4x-5.

$$\left(12x-15\right)\left(2x+3\right)-1+\left(x+2\right)\left(2x+3\right)$$

Apply the distributive property by multiplying each term of 12x-15 by each term of 2x+3.

$$24x^{2}+36x-30x-45-1+\left(x+2\right)\left(2x+3\right)$$

Combine 36x and -30x to get 6x.

$$24x^{2}+6x-45-1+\left(x+2\right)\left(2x+3\right)$$

Subtract 1 from -45 to get -46.

$$24x^{2}+6x-46+\left(x+2\right)\left(2x+3\right)$$

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

$$24x^{2}+6x-46+2x^{2}+3x+4x+6$$

Combine 3x and 4x to get 7x.

$$24x^{2}+6x-46+2x^{2}+7x+6$$

Combine 24x^{2} and 2x^{2} to get 26x^{2}.

$$26x^{2}+6x-46+7x+6$$

Combine 6x and 7x to get 13x.

$$26x^{2}+13x-46+6$$

Add -46 and 6 to get -40.

$$26x^{2}+13x-40$$

Expand

$$26x^{2}+13x-40$$

Solution Steps

Use the distributive property to multiply 3 by 4x-5.

$$\left(12x-15\right)\left(2x+3\right)-1+\left(x+2\right)\left(2x+3\right)$$

Apply the distributive property by multiplying each term of 12x-15 by each term of 2x+3.

$$24x^{2}+36x-30x-45-1+\left(x+2\right)\left(2x+3\right)$$

Combine 36x and -30x to get 6x.

$$24x^{2}+6x-45-1+\left(x+2\right)\left(2x+3\right)$$

Subtract 1 from -45 to get -46.

$$24x^{2}+6x-46+\left(x+2\right)\left(2x+3\right)$$

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

$$24x^{2}+6x-46+2x^{2}+3x+4x+6$$

Combine 3x and 4x to get 7x.

$$24x^{2}+6x-46+2x^{2}+7x+6$$

Combine 24x^{2} and 2x^{2} to get 26x^{2}.

$$26x^{2}+6x-46+7x+6$$

Combine 6x and 7x to get 13x.

$$26x^{2}+13x-46+6$$

Add -46 and 6 to get -40.

$$26x^{2}+13x-40$$