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

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

Evaluate

$$18-12x-3x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 3x^{2} and -6x^{2} to get -3x^{2}.

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

Add 12 and 6 to get 18.

$$-3x^{2}-12x+18$$

Expand

$$18-12x-3x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 3x^{2} and -6x^{2} to get -3x^{2}.

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

Add 12 and 6 to get 18.

$$-3x^{2}-12x+18$$