Solve (-4a-b^4)(-4a+b^4)

$$( - 4 a - b ^ { 4 } ) ( - 4 a + b ^ { 4 } )$$

Evaluate

$$16a^{2}-b^{8}$$

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}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(-4a\right)^{2}-b^{8}$$

Expand \left(-4a\right)^{2}.

$$\left(-4\right)^{2}a^{2}-b^{8}$$

Calculate -4 to the power of 2 and get 16.

$$16a^{2}-b^{8}$$

Expand

$$16a^{2}-b^{8}$$

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}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(-4a\right)^{2}-b^{8}$$

Expand \left(-4a\right)^{2}.

$$\left(-4\right)^{2}a^{2}-b^{8}$$

Calculate -4 to the power of 2 and get 16.

$$16a^{2}-b^{8}$$