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

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

Evaluate

$$1-2b-b^{2}$$

Solution Steps

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

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

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

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

Multiply -1 and -1 to get 1.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$b^{2}\left(-b\right)-b-b+b^{3}+1-b^{2}$$

Combine -b and -b to get 2\left(-b\right).

$$b^{2}\left(-b\right)+2\left(-b\right)+b^{3}+1-b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$b^{3}\left(-1\right)+2\left(-1\right)b+b^{3}+1-b^{2}$$

Multiply 2 and -1 to get -2.

$$b^{3}\left(-1\right)-2b+b^{3}+1-b^{2}$$

Combine b^{3}\left(-1\right) and b^{3} to get 0.

$$-2b+1-b^{2}$$

Expand

$$1-2b-b^{2}$$

Solution Steps

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

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

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

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

Multiply -1 and -1 to get 1.

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

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$b^{2}\left(-b\right)-b-b+b^{3}+1-b^{2}$$

Combine -b and -b to get 2\left(-b\right).

$$b^{2}\left(-b\right)+2\left(-b\right)+b^{3}+1-b^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$b^{3}\left(-1\right)+2\left(-1\right)b+b^{3}+1-b^{2}$$

Multiply 2 and -1 to get -2.

$$b^{3}\left(-1\right)-2b+b^{3}+1-b^{2}$$

Combine b^{3}\left(-1\right) and b^{3} to get 0.

$$-2b+1-b^{2}$$