Final answer:
To simplify (2√5 - 4)(3√5 + 2), use the distributive property to expand the expression and combine like terms, resulting in the simplified form 22 - 8√5.
Step-by-step explanation:
To simplify the expression (2√5 - 4)(3√5 + 2), we apply the distributive property (also known as the FOIL method in the context of binomials). This involves multiplying each term in the first binomial by each term in the second binomial.
- Multiply the first terms: (2√5) * (3√5) = 6 * 5 = 30
- Multiply the outer terms: (2√5) * 2 = 4√5
- Multiply the inner terms: (-4) * (3√5) = -12√5
- Multiply the last terms: (-4) * 2 = -8
Combine these results to get the expression: 30 + 4√5 - 12√5 - 8. Combine like terms (4√5 and -12√5) to simplify further:
30 - 8√5 - 8 = 22 - 8√5.
Therefore, the simplified form of the expression is 22 - 8√5.