Answer:
True
True
Step-by-step explanation:
Let's expand the parentheses for each problem.
1. [tex](x\sqrt{3} +y)(x\sqrt{3} -y)[/tex]; use FOIL (first, outer, inner, last):
[tex](x\sqrt{3} +y)(x\sqrt{3} -y)=(x\sqrt{3})^2+x\sqrt{3}*y-x\sqrt{3}*y+y*(-y)=3x^2-y^2[/tex]
This matches the first part, so it's true.
2. [tex](3a+bi)(3a-bi)[/tex]; use FOIL again. Remember that the i is imaginary and means [tex]\sqrt{-1}[/tex].
[tex](3a+bi)(3a-bi)=(3a)^2-3abi+3abi+(bi)*(-bi)=9a^2-b^2*(-1)[/tex]
[tex]9a^2-b^2*(-1)=9a^2+b^2[/tex]
So, this is true, too.
Hope this helps!
