To determine which among the given expressions is equivalent to the target expression [tex]\( 17x(1 - y) \)[/tex], let's carefully examine and compare each one with [tex]\( 17x(1 - y) \)[/tex]:
1. First expression: [tex]\( 17x(1 + y) \)[/tex]
[tex]\[
17x(1 + y)
\][/tex]
This expression clearly has a positive [tex]\( y \)[/tex] inside the parentheses, which means it is not equivalent to [tex]\( 17x(1 - y) \)[/tex].
2. Second expression: [tex]\( 17x(1 - 2y) \)[/tex]
[tex]\[
17x(1 - 2y)
\][/tex]
This expression has [tex]\( -2y \)[/tex] inside the parentheses, different from [tex]\( -y \)[/tex] in the target expression, so it is not an equivalent expression.
3. Third expression: [tex]\( 17x(1 - y) \)[/tex]
[tex]\[
17x(1 - y)
\][/tex]
This expression matches exactly with the target expression. Therefore, it is indeed an equivalent expression.
4. Fourth expression: [tex]\( 17x(1 + 2y) \)[/tex]
[tex]\[
17x(1 + 2y)
\][/tex]
This expression has [tex]\( +2y \)[/tex] inside the parentheses, which again is different from the target expression [tex]\( 17x(1 - y) \)[/tex], so it is not equivalent.
After examining all the given options, the third expression, [tex]\( 17x(1 - y) \)[/tex], is indeed equivalent to the target expression [tex]\( 17x(1 - y) \)[/tex].
Thus, the correct choice is:
[tex]\[
3
\][/tex]
