Solve (-p^2-q^3)(-p^2+q^3)

$$( - p ^ { 2 } - q ^ { 3 } ) ( - p ^ { 2 } + q ^ { 3 } )$$

Evaluate

$$p^{4}-q^{6}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(-p^{2}\right)^{2}-\left(q^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-p^{2}\right)^{2}-q^{6}$$

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

$$\left(p^{2}\right)^{2}-q^{6}$$

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

$$p^{4}-q^{6}$$

Expand

$$p^{4}-q^{6}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(-p^{2}\right)^{2}-\left(q^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-p^{2}\right)^{2}-q^{6}$$

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

$$\left(p^{2}\right)^{2}-q^{6}$$

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

$$p^{4}-q^{6}$$