Question

Expand the expression (1x/2 - 2y/3 - 4z/5)².

a) 1x²/4 - 2xy/3 + 4y²/9 - 4xz/5 - 16yz/15 + 16z²/25
b) 1x²/4 - 2xy/3 + 4y²/9 - 4xz/5 + 16yz/15 - 16z²/25
c) 1x²/4 - 4xy/3 + 4y²/9 - 4xz/5 - 16yz/15 + 16z²/25
d) 1x²/4 - 4xy/3 + 4y²/9 - 4xz/5 + 16yz/15 - 16z²/25

Answer 1

To expand the expression (1x/2 - 2y/3 - 4z/5)², we can use the FOIL method. The expanded expression is 1x²/4 - 2xy/3 + 4y²/9 - 4xz/5 - 16yz/15 + 16z²/25.

Step-by-step explanation:

To expand the expression (1x/2 - 2y/3 - 4z/5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. Here are the steps:

1. Multiply the first terms in each parentheses: (1x/2)*(1x/2) = 1x²/4
2. Multiply the outer terms: (1x/2)*(-4z/5) = -4xz/5
3. Multiply the inner terms: (-2y/3)*(1x/2) = -2xy/3
4. Multiply the last terms in each parentheses: (-2y/3)*(-4z/5) = 16yz/15
5. Simplify each of the resulting terms: (-2y/3)*(-2y/3) = 4y²/9
6. Simplify any like terms: 1x²/4 - 2xy/3 + 4y²/9 - 4xz/5 - 16yz/15
7. Finally, combine all the terms: 1x²/4 - 2xy/3 + 4y²/9 - 4xz/5 - 16yz/15 + 16z²/25