Answer:
The answer is 22 - 8√5 ⇒ (d)
Step-by-step explanation:
* Lets revise the foil method which used in multiplication
of two binomial
- If (a+ b)(c + d), then we do that
# a × c = ac and b × d = bd
# b × c = bc and a × d = ad
∴ (a+ b)(c + d) = ac + ad + bc + bd
- We called bc means and ad extremes, in most problems they
are like terms and we add them
* Now lets solve the problem
∵ (2√5 - 4)(3√5 + 2)
# 2√5 × 3√5 = (2 × 3) × (√5 × √5) = 6 × 5 = 30
# -4 × 2 = -8
* 30 and -8 are like terms we add them
# 30 + -8 = 22
# Extremes ⇒ 2√5 × 2 = (2 × 2) × √5 = 4√5
# Means ⇒ -4 × 3√5 = (-4 × 3) × √5 = -12√5
* 4√5 and -12√5 are like terms we will add them
# 4√5 + -12√5 = -8√5
∴ (2√5 - 4)(3√5 + 2) = 22 + -8√5 = 22 - 8√5
