Question

identify the properties of addition and multiplication in the following-
A) [(-7)x(-3)] (4)=-7x[(-3)x4]
B) 4+[(-3)+12]=[4+(-3)]+12
C) 6[(-3)+6]=6x(-3))+6x6

Answer 1

A  associative property of addition
B   associative property of multiplication
C  distributive property of multiplication

Answer 2

A) [(-7) x (-3)] (4)=-7 x [(-3) x 4]
LHS = [(-7) x (-3)] x (4) = [21] x 4 = 84
RHS = -7 x [(-3) x 4] = -7 x [-12] = 84
So LHS = RHS
Associative property

B) 4+[(-3)+12]=[4+(-3)]+12
LHS = 4+[(-3)+12] = 4 + [12-3] = 4 + 9 = 13
RHS = [4+(-3)]+12 = [4-3] + 12 = 1 + 12 = 13
LHS = RHS
Associative property

C) 6[(-3)+6]=6x(-3))+6x6
LHS = 6[(-3)+6] = 6 x [6-3] = 6 x 3 = 18
RHS = 6x(-3))+6x6 = (-18) + 36 = 36 - 18 = 18
LHS = RHS
Distributive Property