Final answer:
The product of (5√2 - 4√3)(5√2 - 4√3) is found using the distributive property. After multiplying and combining like terms, the result is 98 - 40√6.
Step-by-step explanation:
To find the product of (5√2 - 4√3)(5√2 - 4√3), we apply the distributive property (also known as the FOIL method for binomials), which stands for First, Outer, Inner, Last:
- First: Multiply the first terms in each binomial: (5√2)(5√2) = 25·2 = 50.
- Outer: Multiply the outer terms in each binomial: (5√2)(-4√3) = -20√6.
- Inner: Multiply the inner terms in each binomial: (-4√3)(5√2) = -20√6.
- Last: Multiply the last terms in each binomial: (-4√3)(-4√3) = 16·3 = 48.
Combine these results: 50 - 20√6 - 20√6 + 48. The like terms here are the two -20√6 terms. Combine them to get -40√6.
The final answer is 50 + 48 - 40√6 = 98 - 40√6.
Therefore, the product is “98 - 40√6”, which simplifies to this exact form.