the following steps are used to rewrite the polynomial expression 3(x+4y)+5(2x-y)
step 1: (3x+12y)+(10x-5y)
step 2: (3x+12y)+(-5y+10x)
step 3: 3x+(12y-5y)+10x
step 4: 3x+10x+(12y-5y)
step 5: 13x+7y
identify the property used in each of the steps:
step 1
step 2
step 3
step 4
Step 1: Distributive property
Step 2: Commutative property
Step 3: Associative property
Step 4: Commutative property and combining like terms
why
Step 1: The distributive property was used to remove the parentheses by multiplying each term inside the parentheses by the integer outside the parentheses.
Step 2: The commutative property of addition was used to change the order of the terms within the parentheses.
Step 3: The associative property was used to regroup the terms by rearranging the operations.
Step 4: The commutative property of addition was used to change the order of the terms within the final expression, and like terms were combined to simplify the expression.