How do you solve (5√2+3√5)(2√10-5)

5 (sqrt(2) + sqrt(5))

Step-by-step explanation:

Simplify the following:

(5 sqrt(2) + 3 sqrt(5)) (2 sqrt(10) - 5)

Hint: | Multiply 5 sqrt(2) + 3 sqrt(5) and 2 sqrt(10) - 5 together using FOIL.

(5 sqrt(2) + 3 sqrt(5)) (2 sqrt(10) - 5) = (5 sqrt(2)) (-5) + (5 sqrt(2)) (2 sqrt(10)) + (3 sqrt(5)) (-5) + (3 sqrt(5)) (2 sqrt(10)):

-5×5 sqrt(2) + 5 sqrt(2)×2 sqrt(10) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply -5 and 5 together.

-5×5 = -25:

-25 sqrt(2) + 5 sqrt(2)×2 sqrt(10) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply 5 and 2 together.

5×2 = 10:

-25 sqrt(2) + 10 sqrt(2) sqrt(10) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(10).

sqrt(2) sqrt(10) = sqrt(2×10):

-25 sqrt(2) + 10 sqrt(2×10) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply 2 and 10 together.

2×10 = 20:

-25 sqrt(2) + 10 sqrt(20) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Simplify radicals.

sqrt(20) = sqrt(2^2×5) = 2 sqrt(5):

-25 sqrt(2) + 10×2 sqrt(5) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply 10 and 2 together.

10×2 = 20:

-25 sqrt(2) + 20 sqrt(5) - 5×3 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply -5 and 3 together.

-5×3 = -15:

-25 sqrt(2) + 20 sqrt(5) + -15 sqrt(5) + 3 sqrt(5)×2 sqrt(10)

Hint: | Multiply 3 and 2 together.

3×2 = 6:

-25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 6 sqrt(5) sqrt(10)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(5) sqrt(10).

sqrt(5) sqrt(10) = sqrt(5×10):

-25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 6 sqrt(5×10)

Hint: | Multiply 5 and 10 together.

5×10 = 50:

-25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 6 sqrt(50)

Hint: | Simplify radicals.

sqrt(50) = sqrt(2×5^2) = 5 sqrt(2):

-25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 6×5 sqrt(2)

Hint: | Multiply 6 and 5 together.

6×5 = 30:

-25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 30 sqrt(2)

Hint: | Add the numbers in -25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 30 sqrt(2) together.

Add like terms. -25 sqrt(2) + 20 sqrt(5) - 15 sqrt(5) + 30 sqrt(2) = 5 sqrt(2) + 5 sqrt(5):

5 sqrt(2) + 5 sqrt(5)

Hint: | Factor common terms from 5 sqrt(2) + 5 sqrt(5).

Factor 5 out of 5 sqrt(2) + 5 sqrt(5) giving 5 (sqrt(2) + sqrt(5)):

5 (sqrt(2) + sqrt(5))