Question 2 (Matching Worth 10 points)
(06.02)

Match the verbal expression (term) with its algebraic expression (definition).

Term Definition
Some number increased by two A) a ÷ 2
A variable decreased by two B) b + 2
Product of unknown value and two C) y2
The quotient of some number and two D) 2z
An unknown value squared E) x − 2

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81