Solve left(1+6xright)left(2+3xright)-left(2-3xright)^2-(-3x-1)

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

Evaluate

$$9x^{2}+30x-1$$

Solution Steps

Use the distributive property to multiply 1+6x by 2+3x and combine like terms.

$$2+15x+18x^{2}-\left(2-3x\right)^{2}-\left(-3x-1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-3x\right)^{2}.

$$2+15x+18x^{2}-\left(4-12x+9x^{2}\right)-\left(-3x-1\right)$$

To find the opposite of 4-12x+9x^{2}, find the opposite of each term.

$$2+15x+18x^{2}-4+12x-9x^{2}-\left(-3x-1\right)$$

Subtract 4 from 2 to get -2.

$$-2+15x+18x^{2}+12x-9x^{2}-\left(-3x-1\right)$$

Combine 15x and 12x to get 27x.

$$-2+27x+18x^{2}-9x^{2}-\left(-3x-1\right)$$

Combine 18x^{2} and -9x^{2} to get 9x^{2}.

$$-2+27x+9x^{2}-\left(-3x-1\right)$$

To find the opposite of -3x-1, find the opposite of each term.

$$-2+27x+9x^{2}+3x+1$$

Combine 27x and 3x to get 30x.

$$-2+30x+9x^{2}+1$$

Add -2 and 1 to get -1.

$$-1+30x+9x^{2}$$

Expand

$$9x^{2}+30x-1$$

Solution Steps

Use the distributive property to multiply 1+6x by 2+3x and combine like terms.

$$2+15x+18x^{2}-\left(2-3x\right)^{2}-\left(-3x-1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-3x\right)^{2}.

$$2+15x+18x^{2}-\left(4-12x+9x^{2}\right)-\left(-3x-1\right)$$

To find the opposite of 4-12x+9x^{2}, find the opposite of each term.

$$2+15x+18x^{2}-4+12x-9x^{2}-\left(-3x-1\right)$$

Subtract 4 from 2 to get -2.

$$-2+15x+18x^{2}+12x-9x^{2}-\left(-3x-1\right)$$

Combine 15x and 12x to get 27x.

$$-2+27x+18x^{2}-9x^{2}-\left(-3x-1\right)$$

Combine 18x^{2} and -9x^{2} to get 9x^{2}.

$$-2+27x+9x^{2}-\left(-3x-1\right)$$

To find the opposite of -3x-1, find the opposite of each term.

$$-2+27x+9x^{2}+3x+1$$

Combine 27x and 3x to get 30x.

$$-2+30x+9x^{2}+1$$

Add -2 and 1 to get -1.

$$-1+30x+9x^{2}$$