how would you factor (5(x+2)^4)+(3x(x+2)^3)-(2x(x+2)^2).
I have so far gotten it down to 2(3x^4+25x^3+74x^2+92x+40) but i'm not sure that i am doing this right.
you went the wrong way, you expanded.
notice the common factor of (x+2)^2
so your expression is
(x+2)^2[5(x+2)^2 + 3x(x+2) - 2x]
now expand the square bracket, since I don't see any more common factors
= (x+2)^2[5x^2 + 20x + 20 + 3x^2 + 6x - 2x]
=(x+2)^2[8x^2 + 24x + 20]
= 4(x+2)^2(2x^2 + 6x + 5)
I'm building a new fence around my yard. The length is 20 ft. The width is 18 ft long. How much will I need to enclose the entire space
To factor the expression (5(x+2)^4) + (3x(x+2)^3) - (2x(x+2)^2), we will start by factoring out the common factor, which is (x+2)^2. This is done by finding the greatest common factor of the terms inside the parentheses.
First, let's look at the terms inside the parentheses individually:
Term 1: 5(x+2)^4.
Term 2: 3x(x+2)^3.
Term 3: -2x(x+2)^2.
The greatest common factor among these terms is (x+2)^2. So, we can factor it out as follows:
(x+2)^2 * [5(x+2)^2 + 3x(x+2) - 2x].
Next, we simplify the remaining expression inside the bracket:
5(x+2)^2 + 3x(x+2) - 2x.
Expanding the terms inside, we get:
5(x^2 + 4x + 4) + 3x^2 + 6x - 2x.
Simplifying further:
5x^2 + 20x + 20 + 3x^2 + 4x - 2x.
Combining like terms:
8x^2 + 22x + 20.
Finally, we plug this simplified expression back into our factored form:
(x+2)^2 * (8x^2 + 22x + 20).
So, the factored form of the expression (5(x+2)^4) + (3x(x+2)^3) - (2x(x+2)^2) is (x+2)^2 * (8x^2 + 22x + 20).
As for your intermediate step, it seems like you made a small error while factoring out the common factor. Instead of factoring out 2, you factored out 2(x+2)^2, which is if we continue from there also correct but it doesn't simplify the expression to the most reduced form.