Solve 3left(6x+1right)^2-(6x+1)(5x-9)

$$3 { \left(6x+1 \right) }^{ 2 } -(6x+1)(5x-9)$$

Evaluate

$$\left(6x+1\right)\left(13x+12\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+1\right)^{2}.

$$3\left(36x^{2}+12x+1\right)-\left(6x+1\right)\left(5x-9\right)$$

Use the distributive property to multiply 3 by 36x^{2}+12x+1.

$$108x^{2}+36x+3-\left(6x+1\right)\left(5x-9\right)$$

Use the distributive property to multiply 6x+1 by 5x-9 and combine like terms.

$$108x^{2}+36x+3-\left(30x^{2}-49x-9\right)$$

To find the opposite of 30x^{2}-49x-9, find the opposite of each term.

$$108x^{2}+36x+3-30x^{2}+49x+9$$

Combine 108x^{2} and -30x^{2} to get 78x^{2}.

$$78x^{2}+36x+3+49x+9$$

Combine 36x and 49x to get 85x.

$$78x^{2}+85x+3+9$$

Add 3 and 9 to get 12.

$$78x^{2}+85x+12$$

Expand

$$78x^{2}+85x+12$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6x+1\right)^{2}.

$$3\left(36x^{2}+12x+1\right)-\left(6x+1\right)\left(5x-9\right)$$

Use the distributive property to multiply 3 by 36x^{2}+12x+1.

$$108x^{2}+36x+3-\left(6x+1\right)\left(5x-9\right)$$

Use the distributive property to multiply 6x+1 by 5x-9 and combine like terms.

$$108x^{2}+36x+3-\left(30x^{2}-49x-9\right)$$

To find the opposite of 30x^{2}-49x-9, find the opposite of each term.

$$108x^{2}+36x+3-30x^{2}+49x+9$$

Combine 108x^{2} and -30x^{2} to get 78x^{2}.

$$78x^{2}+36x+3+49x+9$$

Combine 36x and 49x to get 85x.

$$78x^{2}+85x+3+9$$

Add 3 and 9 to get 12.

$$78x^{2}+85x+12$$