In the given polynomial expression: (x+5) + 3(a + (6x)y), the steps for rewriting it are as follows:
Step 1: Rearrange the terms in the expression.
3(a + (6x)y) + (x+5)
Step 2: Distribute the 3 across the terms within the parentheses.
3(a+y(6x)) + (x+5)
Step 3: Simplify by multiplying y with 6x.
3a + y(18x) + (x+5)
In each step, different properties of algebra are utilized. In Step 1, the property of associative addition is applied, allowing the rearrangement of terms without changing the sum. Step 2 involves the distributive property, which enables the multiplication of a factor across terms inside parentheses. Finally, Step 3 demonstrates the combination of like terms, using the property of combining like terms in algebra to simplify the expression.
By identifying and understanding the properties used in each step, you can effectively manipulate algebraic expressions and solve equations more efficiently.
