Question

John claims the following two equations are equivalent:

−
2
(
5
y
−
3
)
=
−
10
y
−
6


John's work in determining an expression equivalent to the first expression is shown below.

−
2
(
5
y
−
3
)

=
(
−
2
⋅
5
y
)
−
(
−
2
⋅
−
3
)

=
−
10
y
−
6


Which statement explains why John's claim is incorrect?

Answer 1

John applied the distributive property incorrectly. When you distribute −2 across (5y − 3) you get

−2(5y − 3) = (−2)(5y) + (−2)(−3) = −10y + 6.

John wrote a minus between the two products and got −10y − 6, but (−2)(−3) = +6, not −6.