Question

How do you distribute 7(2x^2+9x-3)

Answer 1

First, when dealing with the Distributive Property, we always need to pay attention to what number/variable we are multiplying by.
The concept of the Distributive Property is to look at the number/variable outside of the parenthesis and then multiply it by all numbers/variables inside of the parenthesis individually, and then sum those products up.

If you're having trouble grasping this concept, here's an example:

Ex:
2(1 + 3)
Multiply the number outside of the parenthesis (2) by all numbers inside of the parenthesis (1 and 3) individually.
2*(1) + 2*(3)
Simplify the multiplication process.
2 + 6
Sum up our products.
8.
8 is our answer for this example.

Now that we've explained and practiced what we are working on, let's apply this concept to the real problem.

7(2x^2 + 9x - 3)
Multiply the number outside of the parenthesis (7) by all numbers/variables inside of the parenthesis (2x^2, 9x, and -3).
7(2x^2) + 7(9x) + 7(-3)
Simplify the first multiplication parenthesis.
7*2x^2 = 14x^2
Simplify the second multiplication parenthesis.
7*9x = 21x
Simplify the third and final multiplication parenthesis.
7*(-3) = -21 (When you multiply a positive by a negative, your product is negative).

Now, let's write down our final products as a whole answer. Remember to start from the highest exponent.

14x^2 + 21x - 21 is your final expression.

I hope this helps! Let me know if you have any questions or concerns down in the comment box below this answer, and I'll get back to you when I can.
-Ekansh Nimbalkar