Final answer:
The distributive property is used to multiply each term inside the parentheses by the factor outside, yielding 124 for the first expression, -24m + 18 for the second, -14 - 26a for the third, and 28 for the fourth.
Step-by-step explanation:
To apply the distributive property to the expressions provided, we will multiply each term inside the parentheses by the factor outside, and then combine all like terms where applicable.
First Expression
4(40 - 9)
= (4 × 40) - (4 × 9)
= 160 - 36
= 124
Second Expression
-3(8m - 6)
= (-3 × 8m) - (-3 × 6)
= -24m + 18
Third Expression
(7 + 13a)(-2)
= (7 × -2) + (13a × -2)
= -14 - 26a
Fourth Expression
-(2 - 30)
= -(+2) - (-30)
= -2 + 30
= 28
In every step, we have followed the sign multiplication rules and used the distributive property to expand each expression.