Which property justifies each step in all of these? Of these ten: www.analyzemath.com/algebra/rules_algebra.html
I got all of them wrong and can't find out why
1. 6a + (8b + 2a)
= (6a + 2a) +8b
2. (6a + 2a) + 8b
= (6 + 2)a + 8b
3. (6 + 2)a + 8b
= 8a + 8b
4. 8a2 + (8a + a2) + 7a
= 8a2 + (a2 + 8a) + 7a
all wrong? Man -- there are only about four properties!
#1 Associative: (a+b)+c = a+(b+c)
#2 Distributive: a(b+c) = ab + ac
#3 ditto
#4 Commutative: a+b = b+a
Time to review the section, eh?
Thank you! I see that there's more than four on the list though...
8a2 + (a2 + 8a) + 7a
= (8a2 + a2) + 8a + 7a
what property is this and how do you know?
To justify each step in the given expressions, you need to understand the properties and rules of algebra. Let's go through each step and explain the reasoning behind them:
1. 6a + (8b + 2a) = (6a + 2a) + 8b
To simplify the expression, we can use the associative property. The associative property states that the grouping of numbers or variables doesn't affect the sum or product. In this case, we can rearrange the terms within the parentheses to make it easier to combine like terms.
2. (6a + 2a) + 8b = (6 + 2)a + 8b
Applying the distributive property here, we are distributing the common factor (a) to both terms inside the parentheses. The distributive property states that when a number or variable is multiplied by a sum or a difference, it can be distributed to each term within the parentheses.
3. (6 + 2)a + 8b = 8a + 8b
By simplifying the expression further, we can add the coefficients of the like terms. In this case, the terms (6 + 2)a become 8a because we added the coefficients of a. The same applies to the constant term 8b.
4. 8a2 + (8a + a2) + 7a = 8a2 + (a2 + 8a) + 7a
Once again, we can apply the associative property to rearrange the terms within the parentheses. This step helps to group like terms together and make it easier to combine them.
Remember, the key to solving algebraic expressions is to apply the properties and rules consistently. Practice and understanding these properties will help you solve expressions confidently.