This lesson gives you a list of nine important properties for simplifying algebraic expressions.
Let a,b,and c represent real numbers.
Definition of subtraction : a - b = a + (-b)
Definition of division : a ÷ b = a/b = a × 1/b, b ≠ 0
Multiplication by zero : 0 × a = 0
Multiplication by -1 : -1 × a = -a
Distributive property for subtraction : a(b - c) = ab - ac
Opposite of a difference : -(a - b) = b - a
Opposite of a sum : -(a + b) = -a + -b
Opposite of a product : -(ab) = -a × b = a × -b
Opposite of an opposite : -(-a) = a
Match the equation with the appropriate property name
A. 4(x - y) = 4x - 4y
B. (x - 2) ÷ 5z = (x - 2) / 5z
C. -(t-1) = -1(t-1)
D. 2d - 7 = 2d + (-7)
E. -( 2d - 7) = 7 - 2d
F. -[-(8 + s)] = 8 + s
G. -(12xy) = 12(-xy)
H. -[3 + (-a)] = -3 + [-(-a)]
I. (10x2 - 15y)(0) + -x = 0 + -x
1. Definition of division
2. Opposite of a sum
3. Opposite of an opposite
4. Opposite of a product
5. Multiplication by zero
6. Multiplication by -1
7. Opposite of a difference
8. Distributive property for subtraction
9. Definition of subtraction