### Instruction: Simplify $(x+15)+(100x+15)$.### Response: To simplify an expression with parentheses, I can first try to remove them by applying the distributive property of addition over multiplication.
This means that I can multiply the factor outside the parentheses by each term inside the parentheses, and then add up the results.
For example, $(x+15)+(100x+15)$ is equivalent to $(1\times x+1\times 15)+(100\times x+100\times 15)$ by multiplying each term by 1 or 100.
Next, I can simplify the multiplications by applying the commutative and associative properties of multiplication, which allow me to rearrange and regroup the factors without changing the product.
For example, $1\times x$ is the same as $x\times 1$, and $100\times x$ is the same as $x\times 100$, so I can write $(x+15)+(100x+15)$ as $(x\times 1+15\times 1)+(x\times 100+15\times 100)$.
Then, I can multiply the numbers together, since they are constants and I know their values.
For example, $15\times 1=15$ and $15\times 100=1500$, so I can write $(x\times 1+15\times 1)+(x\times 100+15\times 100)$ as $(x+15)+(100x+1500)$.
Now, I have removed the parentheses, but I still have to simplify the expression further by combining the like terms, which are the terms that have the same variable and exponent.
In this case, the like terms are $x$ and $100x$, since they both have the variable $x$ raised to the power of 1.
I can add them together by adding their coefficients, which are the numbers in front of the variable.
For example, $x+100x$ is the same as $(1+100)x$, since I can factor out the common factor of $x$ and apply the distributive property in reverse.
Then, I can add 1 and 100, which gives me 101.
So, $x+100x=(1+100)x=101x$.
The other terms, $15$ and $1500$, are also like terms, since they are both constants with no variables.
I can add them together by adding their values, which gives me 1515.
So, $15+1500=1515$.
Finally, I can write the simplified expression by joining the two terms with a plus sign.
So, $(x+15)+(100x+15)=101x+1515$.