Solve b(x^2-1)-b(x-1)^2

$$b ( x ^ { 2 } - 1 ) - b ( x - 1 ) ^ { 2 }$$

Evaluate

$$2b\left(x-1\right)$$

Solution Steps

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

$$bx^{2}-b-b\left(x-1\right)^{2}$$

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

$$bx^{2}-b-b\left(x^{2}-2x+1\right)$$

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

$$bx^{2}-b-\left(bx^{2}-2bx+b\right)$$

To find the opposite of bx^{2}-2bx+b, find the opposite of each term.

$$bx^{2}-b-bx^{2}+2bx-b$$

Combine bx^{2} and -bx^{2} to get 0.

$$-b+2bx-b$$

Combine -b and -b to get -2b.

$$-2b+2bx$$

Expand

$$2bx-2b$$

Solution Steps

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

$$bx^{2}-b-b\left(x-1\right)^{2}$$

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

$$bx^{2}-b-b\left(x^{2}-2x+1\right)$$

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

$$bx^{2}-b-\left(bx^{2}-2bx+b\right)$$

To find the opposite of bx^{2}-2bx+b, find the opposite of each term.

$$bx^{2}-b-bx^{2}+2bx-b$$

Combine bx^{2} and -bx^{2} to get 0.

$$-b+2bx-b$$

Combine -b and -b to get -2b.

$$-2b+2bx$$