Question

Katrina is asked to simplify the expression Negative 3 a minus 4 b minus 2 (5 a minus 7 b).

She writes: Negative 3 a minus 4 b minus 2 (5 a minus 7 b) = negative 3 a minus 4 b minus 10 a + 14 b

Which property allows her to do this?
the associative property
the commutative property
the distributive property
the additive identity property

Answer 1

Distributive property.

Katrina used the distributive law of multiplication over subtraction: -2(5a − 7b) = (-2)(5a) + (-2)(−7b) = −10a + 14b.