Solve (11v-8w^2)(11v+8w^2)

$$( 11 v - 8 w ^ { 2 } ) ( 11 v + 8 w ^ { 2 } )$$

Evaluate

$$121v^{2}-64w^{4}$$

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}.

$$\left(11v\right)^{2}-\left(8w^{2}\right)^{2}$$

Expand \left(11v\right)^{2}.

$$11^{2}v^{2}-\left(8w^{2}\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$121v^{2}-\left(8w^{2}\right)^{2}$$

Expand \left(8w^{2}\right)^{2}.

$$121v^{2}-8^{2}\left(w^{2}\right)^{2}$$

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

$$121v^{2}-8^{2}w^{4}$$

Calculate 8 to the power of 2 and get 64.

$$121v^{2}-64w^{4}$$

Expand

$$121v^{2}-64w^{4}$$

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}.

$$\left(11v\right)^{2}-\left(8w^{2}\right)^{2}$$

Expand \left(11v\right)^{2}.

$$11^{2}v^{2}-\left(8w^{2}\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$121v^{2}-\left(8w^{2}\right)^{2}$$

Expand \left(8w^{2}\right)^{2}.

$$121v^{2}-8^{2}\left(w^{2}\right)^{2}$$

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

$$121v^{2}-8^{2}w^{4}$$

Calculate 8 to the power of 2 and get 64.

$$121v^{2}-64w^{4}$$