Please help:
Multiply and simplify:
(5sqrt:5 - 10sqrt:3)(2sqrt:5 + 4sqrt:3)
(5sqrt5 - 10sqrt3)(2sqrt5 + 4sqrt3) =
Let a = sqrt5, and b = sqrt3:
(5a - 10b)(2a + 4b).
10a^2 + 20ab - 20ab - 40b^2,
10a^2 - 40b^2,
10(a^2 - 4b^2),
10(a + 2b)(a - 2b),
10(sqrt5 + 2sqrt3)(sqrt5 - 2sqrt3).
To multiply and simplify the given expression, you can use the distributive property.
Step 1: Start by multiplying the first terms of each binomial:
(5sqrt(5) - 10sqrt(3))(2sqrt(5))
= 5sqrt(5) * 2sqrt(5)
= 10 * sqrt(5) * sqrt(5)
= 10 * 5
= 50
Step 2: Next, multiply the outer terms of each binomial:
(5sqrt(5) - 10sqrt(3))(4sqrt(3))
= 5sqrt(5) * 4sqrt(3)
= 20 * sqrt(5) * sqrt(3)
= 20 * sqrt(15)
Step 3: Then, multiply the inner terms of each binomial:
(5sqrt(5) - 10sqrt(3))(-10sqrt(3))
= -10sqrt(3) * 5sqrt(5)
= -50 * sqrt(3) * sqrt(5)
= -50 * sqrt(15)
Step 4: Finally, multiply the last terms of each binomial:
(5sqrt(5) - 10sqrt(3))(-10sqrt(3))
= -10sqrt(3) * -10sqrt(3)
= 100 * 3
= 300
Step 5: Now, add together the products you obtained in Steps 1-4:
50 + 20sqrt(15) - 50sqrt(15) + 300
Step 6: Combine like terms:
50 + 300 + (20sqrt(15) - 50sqrt(15))
= 350 - 30sqrt(15)
Therefore, the simplified expression is 350 - 30sqrt(15).