How do you simplify \[3(x - 2y) + 7(x + 3y) - 3y\] ?

Hint: In this question, we are given an algebraic expression in terms of x and y and we have to simplify it. We will simplify it by using the distributive property. According to the distributive property, the product of a number with the sum of two other numbers is equal to the product of that number with the first number plus the product of that number with the second number, that is, $a(b + c) = ab + ac$ . After simplifying the brackets we will apply the given arithmetic operations.

Complete step-by-step solution:
We have to simplify \[3(x - 2y) + 7(x + 3y) - 3y\]
On applying the distributive property –
\[3(x - 2y) + 7(x + 3y) - 3y = (3 \times x) - (3 \times 2y) + (7 \times x) + (7 \times 3y) - 3y\]
$2y$ represents the product of 2 and y, so $3 \times x = 3x,\,7 \times y = 7y,\,3 \times 2y = 6y$ and $7 \times 3y = 21y$
So, we get –
\[3(x - 2y) + 7(x + 3y) - 3y = 3x - 6y + 7x + 21y - 3y\]
Now, we will group the similar terms, that is, we will write the terms containing “x” side by side and the terms containing “y” side by side –
\[3(x - 2y) + 7(x + 3y) - 3y = 3x + 7x - 6y + 21y - 3y\]
We will again apply the distributive property and take “x” and “y” common –
\[3(x - 2y) + 7(x + 3y) - 3y = x(3 + 7) + y( - 6 + 21 - 3)\]
Now, we will apply the arithmetic operation in the brackets –
\[3(x - 2y) + 7(x + 3y) - 3y = 10x + 12y\]
Hence the simplified form of \[3(x - 2y) + 7(x + 3y) - 3y\] is $10x + 12y$ .

Note: The given expression is called an algebraic expression because it is a combination of numerical values and alphabets. The alphabets in an algebraic expression represent some unknown quantity, so “x” and “y” represent some unknown variable quantity in the given expression. The alphabets and numerical values are linked to each other by some arithmetic operations like addition, subtraction, multiplication and division. The values of the unknown quantities can be obtained with the help of algebraic expressions.