Solve 3b^3*left(-bright)^2-left(-b^2right)^2*(-7b)

$$3 { b }^{ 3 } \times { \left(-b \right) }^{ 2 } - { \left(- { b }^{ 2 } \right) }^{ 2 } \times (-7b)$$

Evaluate

$$10b^{5}$$

Solution Steps

Calculate -b to the power of 2 and get b^{2}.

$$3b^{3}b^{2}-\left(-b^{2}\right)^{2}\left(-7\right)b$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$3b^{5}-\left(-b^{2}\right)^{2}\left(-7\right)b$$

Calculate -b^{2} to the power of 2 and get \left(b^{2}\right)^{2}.

$$3b^{5}-\left(b^{2}\right)^{2}\left(-7\right)b$$

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

$$3b^{5}-b^{4}\left(-7\right)b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$3b^{5}-b^{5}\left(-7\right)$$

Combine 3b^{5} and -b^{5}\left(-7\right) to get 10b^{5}.

$$10b^{5}$$

Expand

$$10b^{5}$$

Solution Steps

Calculate -b to the power of 2 and get b^{2}.

$$3b^{3}b^{2}-\left(-b^{2}\right)^{2}\left(-7\right)b$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$3b^{5}-\left(-b^{2}\right)^{2}\left(-7\right)b$$

Calculate -b^{2} to the power of 2 and get \left(b^{2}\right)^{2}.

$$3b^{5}-\left(b^{2}\right)^{2}\left(-7\right)b$$

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

$$3b^{5}-b^{4}\left(-7\right)b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$3b^{5}-b^{5}\left(-7\right)$$

Combine 3b^{5} and -b^{5}\left(-7\right) to get 10b^{5}.

$$10b^{5}$$