Solve (a^2-b^3)*(a^2+b^3)

$$( a ^ { 2 } - b ^ { 3 } ) \cdot ( a ^ { 2 } + b ^ { 3 } )$$

Evaluate

$$a^{4}-b^{6}$$

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}.

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

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

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

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

$$a^{4}-b^{6}$$

Expand

$$a^{4}-b^{6}$$

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}.

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

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

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

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

$$a^{4}-b^{6}$$