Simplify the expression
(3y+1)^2 + (2y-4)^2
I would start by expanding the two sets of parentheses, then combining like terms. Then take a look at the results and see if it can be factored or otherwise simplified. For example, the first one is
9y^2 + 6y +1.
I also note that a 2 can be factored out of the second set.
Post your work if you get stuck and tell us what you don't understand.
0.03-0.01(x+12)+0.07x=0.02(2x-4)
To simplify the given expression, we need to follow a step-by-step approach. Let's break it down together.
1. Start by expanding the two sets of parentheses using the distributive property.
For the first part, (3y+1)^2, we can rewrite it as (3y+1)(3y+1). Using FOIL (First, Outer, Inner, Last), we can expand it as follows:
(3y+1)(3y+1) = 3y * 3y + 3y * 1 + 1 * 3y + 1 * 1
= 9y^2 + 3y + 3y + 1
= 9y^2 + 6y + 1
Similarly, for the second part, (2y-4)^2, we can rewrite it as (2y-4)(2y-4). Expanding using FOIL:
(2y-4)(2y-4) = 2y * 2y + 2y * (-4) + (-4) * 2y + (-4) * (-4)
= 4y^2 - 8y - 8y + 16
= 4y^2 - 16y + 16
So, the expression becomes:
9y^2 + 6y + 1 + 4y^2 - 16y + 16
2. Next, we need to combine like terms. We can add the coefficients of the like terms together.
Combining the terms, the expression becomes:
(9y^2 + 4y^2) + (6y - 16y) + (1 + 16)
= 13y^2 - 10y + 17
At this point, we have simplified the expression, and it cannot be factored further or simplified any more.