Question

How do you simplify $3u\left( y-3 \right)+\left( y-3 \right)$?

Answer 1

Hint: We separate the variables and the constants of the equation $3u\left( y-3 \right)+\left( y-3 \right)$. We have one multiplication. We multiply the constant and the variable $3u$ with $\left( y-3 \right)$. Then we apply the binary operation of addition and subtraction for both variables and constants. As there are no like terms, we keep the expression as it is.

Complete step by step answer:
The given equation $3u\left( y-3 \right)+\left( y-3 \right)$ is an equation of two variables. We need to simplify the equation by completing the multiplication of the variables separately.
We break the multiplication by multiplying $3u$ with $\left( y-3 \right)$.
So, $3u\left( y-3 \right)=3uy-9u$.
The equation becomes $3u\left( y-3 \right)+\left( y-3 \right)=3uy-9u+\left( y-3 \right)$.
Now we break the parenthesis part. The sign is positive.
So, $3uy-9u+\left( y-3 \right)=3uy-9u+y-3$.
The final result has no like terms. We keep the expression as it is.

Therefore, the simplified form of $3u\left( y-3 \right)+\left( y-3 \right)$ is $3uy-9u+y-3$.

Note: We can verify the result of the equation $3u\left( y-3 \right)+\left( y-3 \right)=3uy-9u+y-3$ by taking the values as $y=4,u=2$.
Therefore, the left-hand side of the equation becomes
\[3u\left( y-3 \right)+\left( y-3 \right)=3\times 2\left( 4-3 \right)+\left( 4-3 \right)=6+1=7\]
The right-hand side of the equation becomes
\[\begin{align}
  & 3uy-9u+y-3 \\
 & =3\times 4\times 2-9\times 2+4-3 \\
 & =24-18+1 \\
 & =7 \\
\end{align}\]
Thus, verified for the equation $3u\left( y-3 \right)+\left( y-3 \right)=3uy-9u+y-3$