Solve (11r+4si)(11r-4si)

$$( 11 r + 4 s i ) ( 11 r - 4 s i )$$

Evaluate

$$121r^{2}+16s^{2}$$

Solution Steps

Multiply 4 and i to get 4i.

$$\left(11r+4is\right)\left(11r-4si\right)$$

Multiply 4 and i to get 4i.

$$\left(11r+4is\right)\left(11r-4is\right)$$

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

$$\left(11r\right)^{2}-\left(4is\right)^{2}$$

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

$$11^{2}r^{2}-\left(4is\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$121r^{2}-\left(4is\right)^{2}$$

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

$$121r^{2}-\left(4i\right)^{2}s^{2}$$

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

$$121r^{2}-\left(-16s^{2}\right)$$

The opposite of -16s^{2} is 16s^{2}.

$$121r^{2}+16s^{2}$$

Expand

$$121r^{2}+16s^{2}$$

Solution Steps

Multiply 4 and i to get 4i.

$$\left(11r+4is\right)\left(11r-4si\right)$$

Multiply 4 and i to get 4i.

$$\left(11r+4is\right)\left(11r-4is\right)$$

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

$$\left(11r\right)^{2}-\left(4is\right)^{2}$$

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

$$11^{2}r^{2}-\left(4is\right)^{2}$$

Calculate 11 to the power of 2 and get 121.

$$121r^{2}-\left(4is\right)^{2}$$

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

$$121r^{2}-\left(4i\right)^{2}s^{2}$$

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

$$121r^{2}-\left(-16s^{2}\right)$$

The opposite of -16s^{2} is 16s^{2}.

$$121r^{2}+16s^{2}$$