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

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

Evaluate

$$12x^{2}+12x-9$$

Solution Steps

Use the distributive property to multiply 6 by 2x-1.

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

Use the distributive property to multiply 12x-6 by 2x+1 and combine like terms.

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

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

$$24x^{2}-6-3\left(4x^{2}-4x+1\right)$$

Use the distributive property to multiply -3 by 4x^{2}-4x+1.

$$24x^{2}-6-12x^{2}+12x-3$$

Combine 24x^{2} and -12x^{2} to get 12x^{2}.

$$12x^{2}-6+12x-3$$

Subtract 3 from -6 to get -9.

$$12x^{2}-9+12x$$

Expand

$$12x^{2}+12x-9$$

Solution Steps

Use the distributive property to multiply 6 by 2x-1.

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

Use the distributive property to multiply 12x-6 by 2x+1 and combine like terms.

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

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

$$24x^{2}-6-3\left(4x^{2}-4x+1\right)$$

Use the distributive property to multiply -3 by 4x^{2}-4x+1.

$$24x^{2}-6-12x^{2}+12x-3$$

Combine 24x^{2} and -12x^{2} to get 12x^{2}.

$$12x^{2}-6+12x-3$$

Subtract 3 from -6 to get -9.

$$12x^{2}-9+12x$$