Solve (b^2-b)^2+4(b^2-b)-12=

$$( b ^ { 2 } - b ) ^ { 2 } + 4 ( b ^ { 2 } - b ) - 12 =$$

Evaluate

$$\left(b-2\right)\left(b+1\right)\left(b^{2}-b+6\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b^{2}-b\right)^{2}.

$$\left(b^{2}\right)^{2}-2b^{2}b+b^{2}+4\left(b^{2}-b\right)-12$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$b^{4}-2b^{2}b+b^{2}+4\left(b^{2}-b\right)-12$$

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

$$b^{4}-2b^{3}+b^{2}+4\left(b^{2}-b\right)-12$$

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

$$b^{4}-2b^{3}+b^{2}+4b^{2}-4b-12$$

Combine b^{2} and 4b^{2} to get 5b^{2}.

$$b^{4}-2b^{3}+5b^{2}-4b-12$$

Expand

$$b^{4}-2b^{3}+5b^{2}-4b-12$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(b^{2}-b\right)^{2}.

$$\left(b^{2}\right)^{2}-2b^{2}b+b^{2}+4\left(b^{2}-b\right)-12$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$b^{4}-2b^{2}b+b^{2}+4\left(b^{2}-b\right)-12$$

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

$$b^{4}-2b^{3}+b^{2}+4\left(b^{2}-b\right)-12$$

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

$$b^{4}-2b^{3}+b^{2}+4b^{2}-4b-12$$

Combine b^{2} and 4b^{2} to get 5b^{2}.

$$b^{4}-2b^{3}+5b^{2}-4b-12$$