Solve 6(2x+1)^2-7(2x+1)-20

$$6 ( 2 x + 1 ) ^ { 2 } - 7 ( 2 x + 1 ) - 20$$

Evaluate

$$\left(4x-3\right)\left(6x+7\right)$$

Solution Steps

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

$$6\left(4x^{2}+4x+1\right)-7\left(2x+1\right)-20$$

Use the distributive property to multiply 6 by 4x^{2}+4x+1.

$$24x^{2}+24x+6-7\left(2x+1\right)-20$$

Use the distributive property to multiply -7 by 2x+1.

$$24x^{2}+24x+6-14x-7-20$$

Combine 24x and -14x to get 10x.

$$24x^{2}+10x+6-7-20$$

Subtract 7 from 6 to get -1.

$$24x^{2}+10x-1-20$$

Subtract 20 from -1 to get -21.

$$24x^{2}+10x-21$$

Expand

$$24x^{2}+10x-21$$

Solution Steps

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

$$6\left(4x^{2}+4x+1\right)-7\left(2x+1\right)-20$$

Use the distributive property to multiply 6 by 4x^{2}+4x+1.

$$24x^{2}+24x+6-7\left(2x+1\right)-20$$

Use the distributive property to multiply -7 by 2x+1.

$$24x^{2}+24x+6-14x-7-20$$

Combine 24x and -14x to get 10x.

$$24x^{2}+10x+6-7-20$$

Subtract 7 from 6 to get -1.

$$24x^{2}+10x-1-20$$

Subtract 20 from -1 to get -21.

$$24x^{2}+10x-21$$