Solve (x-4)^2-3(x-2)(x+1)=

$$( x - 4 ) ^ { 2 } - 3 ( x - 2 ) ( x + 1 ) =$$

Evaluate

$$22-5x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-8x+16-3\left(x-2\right)\left(x+1\right)$$

Use the distributive property to multiply -3 by x-2.

$$x^{2}-8x+16+\left(-3x+6\right)\left(x+1\right)$$

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

$$x^{2}-8x+16-3x^{2}+3x+6$$

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

$$-2x^{2}-8x+16+3x+6$$

Combine -8x and 3x to get -5x.

$$-2x^{2}-5x+16+6$$

Add 16 and 6 to get 22.

$$-2x^{2}-5x+22$$

Expand

$$22-5x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-8x+16-3\left(x-2\right)\left(x+1\right)$$

Use the distributive property to multiply -3 by x-2.

$$x^{2}-8x+16+\left(-3x+6\right)\left(x+1\right)$$

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

$$x^{2}-8x+16-3x^{2}+3x+6$$

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

$$-2x^{2}-8x+16+3x+6$$

Combine -8x and 3x to get -5x.

$$-2x^{2}-5x+16+6$$

Add 16 and 6 to get 22.

$$-2x^{2}-5x+22$$