Answer:
Distributive Property
Explanation:
You want to know what property of arithmetic gets you from -6(7z +(-7z²)) to -42z +42z².
Distributive Property
The distributive property of multiplication over addition means that a factor outside parentheses multiplies each term inside parentheses. This allows parentheses to be eliminated.
-6(7z +(-7z²)) = (-6)(7z) +(-6)(-7z²) = -42z +42z²
This is an application of the distributive property.
Other properties
The commutative property of addition lets you rearrange the order:
a +b = b +a
The associative property of addition lets you change the grouping:
(a +b) +c = a +(b +c)
The multiplicative identity property tells you that multiplication by 1 changes nothing:
1×a = a
The multiplicative inverse property tells you the product of an expression and its inverse is 1.
a×(1/a) = 1 . . . . for a≠0
The commutative and associative properties of multiplication do the same thing as those properties for addition.
ab = ba . . . . commutative property
(ab)c = a(bc) . . . . associative property
The additive identity property of addition tells you adding 0 changes nothing:
0 + a = a
The additive inverse property tells you that the sum of an expression and its inverse is 0.
a + (-a) = 0
The zero factor law tells you a product will be zero if and only if at least one factor is 0.
ab = 0 ⇔ a = 0 and/or b = 0
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Additional comment
It is a good idea to understand these properties, even if you don't remember their names. They form the basis, together with the properties of equality, of all of Algebra.