Question

Help! ASAP- 20 points, easy questions

True or False-
`3x^2 - y^2 = (x√(3) + y) (x√(3) - y)`

True or False-
`9a^2 + b^2 = (3a + bi) (3a - bi)`

Answer 1

1) True

2) True

Explanation:

1) 3x² - y²

(xsqrt(3))² - (y)²

(xsqrt(3) - y)(xsqrt(3) + y)

2) 9a² + b²

9a² - (-b²)

(3a)² - (bi)²

(3a - bi)(3a + bi)

Answer 2

True

True

Explanation:

Let's expand the parentheses for each problem.

1.
`(x√(3) +y)(x√(3) -y)`; use FOIL (first, outer, inner, last):

`(x√(3) +y)(x√(3) -y)=(x√(3))^2+x√(3)*y-x√(3)*y+y*(-y)=3x^2-y^2`

This matches the first part, so it's true.

2.
`(3a+bi)(3a-bi)`; use FOIL again. Remember that the i is imaginary and means
`√(-1)`.

`(3a+bi)(3a-bi)=(3a)^2-3abi+3abi+(bi)*(-bi)=9a^2-b^2*(-1)`

`9a^2-b^2*(-1)=9a^2+b^2`

So, this is true, too.

Hope this helps!