please help me out here the problem is combining like terms.
4x^3-3x^3+9x+2x
I got 1x^3+11x
but when i asked a friend they said it would be x^3+11x
could u help me out please.
also could you tell me if this probem is correct as well (10x^3+6x^2+4x) -(8x^3+2x^2-3x)= 18x^3+4x^2+3x+4
you are both correct
1x^3+11x is the same as x^3+11x
a coefficient of 1 in front of a variable does not have to be written.
so 1a = a
as to your second question
(10x^3+6x^2+4x) -(8x^3+2x^2-3x)
= 10x^3+6x^2+4x-8x^3-2x^2+3x
= x^3 + 4x^2 + 7x
x^3 and 1x^3 are the same thing. The coefficient is just usually left off when it's a 1.
As for the second problem, your answer isn't quite right. Recheck your x^3 and x terms; there should also be no constant term.
Of course, I'd be happy to help you out with combining like terms!
Let's start with the first problem: 4x^3 - 3x^3 + 9x + 2x.
When combining like terms, we group terms that have the same variables raised to the same powers. In this case, we have two terms that both have x^3 as the variable and power: 4x^3 and -3x^3.
To combine these terms, we add their coefficients together. The coefficient of 4x^3 is 4, while the coefficient of -3x^3 is -3.
So, 4x^3 - 3x^3 simplifies to (4 - 3)x^3, which equals 1x^3 or simply x^3.
Next, we have two terms that have x as the variable, but they don't have any powers explicitly written:
9x and 2x.
To combine these terms, we add their coefficients together. The coefficient of 9x is 9, while the coefficient of 2x is 2.
So, 9x + 2x simplifies to (9 + 2)x, which equals 11x.
Now, putting the simplifications together, we have x^3 + 11x. Therefore, your friend is correct!
Regarding the second problem: (10x^3 + 6x^2 + 4x) - (8x^3 + 2x^2 - 3x) = 18x^3 + 4x^2 + 3x + 4.
First, let's distribute the negative sign to all the terms inside the parentheses after the subtraction sign:
10x^3 + 6x^2 + 4x - 8x^3 - 2x^2 + 3x.
Now, let's group the terms with the same variables raised to the same powers:
(10x^3 - 8x^3) + (6x^2 - 2x^2) + (4x + 3x).
The coefficient of 10x^3 is 10, and the coefficient of 8x^3 is 8. Subtracting these, we have (10 - 8)x^3, which equals 2x^3.
The coefficient of 6x^2 is 6, and the coefficient of -2x^2 is -2. Adding these, we have (6 - 2)x^2, which equals 4x^2.
The coefficient of 4x is 4, and the coefficient of 3x is 3. Adding these, we have (4 + 3)x, which equals 7x.
Putting the terms back together, we have:
2x^3 + 4x^2 + 7x.
Therefore, your simplification is not correct. The correct simplification is 2x^3 + 4x^2 + 7x + 4.