Solve (x-1)^2-4(x^2-1)-7x+7

$$( x - 1 ) ^ { 2 } - 4 ( x ^ { 2 } - 1 ) - 7 x + 7$$

Evaluate

$$3\left(1-x\right)\left(x+4\right)$$

Solution Steps

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

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

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

$$x^{2}-2x+1-4x^{2}+4-7x+7$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-2x+1+4-7x+7$$

Add 1 and 4 to get 5.

$$-3x^{2}-2x+5-7x+7$$

Combine -2x and -7x to get -9x.

$$-3x^{2}-9x+5+7$$

Add 5 and 7 to get 12.

$$-3x^{2}-9x+12$$

Expand

$$12-9x-3x^{2}$$

Solution Steps

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

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

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

$$x^{2}-2x+1-4x^{2}+4-7x+7$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-2x+1+4-7x+7$$

Add 1 and 4 to get 5.

$$-3x^{2}-2x+5-7x+7$$

Combine -2x and -7x to get -9x.

$$-3x^{2}-9x+5+7$$

Add 5 and 7 to get 12.

$$-3x^{2}-9x+12$$