Help with math homework?

Question

Hi can you simplify this expression(don't solve just simplify) using '/' for division, '*' for multiplication, and '^' for exponentiation:
(2*sqrt(7)+ 3*sqrt(2))* (sqrt(7)- 5*sqrt(2))

Answer 1

[2√7 + 3√2][√7 - 5√2]

FOIL method: the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms and the Last terms.

2√7(√7) + 2√7(-5√2) + 3√2(√7) + 3√2(-5√2)

2(√7)² - 10(√7)(√2) + 3(√2)(√7) - 15(√2)²

Exponent Laws: (√a)² = a and (√a)(√b) = √(ab)

2(7) - 10√[(7)(2)] + 3√[(7)(2)] - 15(2)

14 - 10√(14) + 3 √(14) - 30

-16 + √(14)[-10 + 3]

-16 + √(14)[-7]

-16 - 7√(14).