Video Transcript
Simplify 11 minus eight 𝑖 multiplied by 11 plus eight 𝑖 plus 13 minus six 𝑖 multiplied by 13 plus six 𝑖.
One way of approaching this question would be to distribute the two pairs of parentheses separately. We could do this using the FOIL method. However, we might notice that both pairs of parentheses are written in the form 𝑎 minus 𝑏𝑖 multiplied by 𝑎 plus 𝑏𝑖. This is our factored expression of the sum of two squares. 𝑎 minus 𝑏𝑖 multiplied by 𝑎 plus 𝑏𝑖 is equal to 𝑎 squared plus 𝑏 squared. This means that 11 minus eight 𝑖 multiplied by 11 plus eight 𝑖 is equal to 11 squared plus eight squared. 11 squared is 121, and eight squared is 64. This means that 11 minus eight 𝑖 multiplied by 11 plus eight 𝑖 is equal to 185.
We can repeat this method for the second set of parentheses. 13 minus six 𝑖 multiplied by 13 plus six 𝑖 is equal to 13 squared plus six squared. 13 squared is equal to 169, and six squared is 36. This means that 13 minus six 𝑖 multiplied by 13 plus six 𝑖 is equal to 205. The simplified version of our expression will therefore be equal to 185 plus 205. This is equal to 390.
11 minus eight 𝑖 multiplied by 11 plus eight 𝑖 plus 13 minus six 𝑖 multiplied by 13 plus six 𝑖 is equal to 390.
