Can you check these questions for me?
1. Add: (3x^4-x+2)+(9x^5-x^2+x)
9x^5+3x^4-x^2+2
2. Add: (4x^3-2x^2+x+4)+(9-x^5-x^2+4x)
-x^5+4x^3-3x^2+13
3. Subtract:(4x^4+3x+x^2)-(x^2-6+3x^3)
4x^4-3x^3+3x+6
4. Subtract: (5x-6)-(3x^3-2x^2)
-3x^3+2x^2+5x-6
5. Subtract: (x-3x^4+2x^2)-(x^3+4x^6)
-4x^6-3x^4+x^3+2x^2-x
6. (x+1)(x^2+x+1)
x^3+2x^2-2x+2
7. (x-1)(x^3+x^2+x)
x^4-x
Thanks in advance!
#5 should be -4x^6-3x^4-x^3+2x^2-x
in #6 how did you get a negative sign?
All terms are positive, should be x^3+2x^2+2x+2
the rest are ok
Sure! Let's check each question together:
1. Add: (3x^4-x+2)+(9x^5-x^2+x)
To add these terms, you need to combine like terms. Here are the steps:
Combine the coefficients of the terms with the same exponent:
3x^4 + 9x^5 = 9x^5 + 3x^4
Combine the coefficients of the terms without any variables:
-1 + 1 = 0
Combine the constant terms:
2
Putting it all together, the sum is: 9x^5 + 3x^4 - x^2 + 2
2. Add: (4x^3-2x^2+x+4)+(9-x^5-x^2+4x)
Similarly, combine like terms:
Combine the coefficients of the terms with the same exponent:
4x^3 + 9 = 9 + 4x^3
Combine the coefficients of the terms without any variables:
-2x^2 + x^2 = -x^2
Combine the coefficients of the terms with the same variable power:
x + 4x = 5x
Combine the constant terms:
4
Putting it all together, the sum is: -x^5 + 4x^3 - 3x^2 + 5x + 13
3. Subtract:(4x^4+3x+x^2)-(x^2-6+3x^3)
To subtract these terms, follow these steps:
Distribute the negative sign to each term in the second parentheses:
4x^4 + 3x + x^2 - x^2 + 6 - 3x^3
Combine the coefficients of the terms with the same exponent:
4x^4 - 3x^3
Combine the coefficients of the terms without any variables:
3x - 3x = 0
Combine the constant terms:
6
Putting it all together, the difference is: 4x^4 - 3x^3 + 6
4. Subtract: (5x-6)-(3x^3-2x^2)
Again, follow these steps:
Distribute the negative sign to each term in the second parentheses:
5x - 6 - 3x^3 + 2x^2
Combine the coefficients of the terms with the same variable power:
5x - 3x^3 + 2x^2
Combine the constant terms:
-6
Putting it all together, the difference is: -3x^3 + 2x^2 + 5x - 6
5. Subtract: (x-3x^4+2x^2)-(x^3+4x^6)
Once more, follow these steps:
Distribute the negative sign to each term in the second parentheses:
x - 3x^4 + 2x^2 - x^3 - 4x^6
Combine the coefficients of the terms with the same variable power:
-4x^6 - 3x^4 - x^3 + 2x^2
Combine the coefficients of the terms without any variables:
x
Putting it all together, the difference is: -4x^6 - 3x^4 + x^3 + 2x^2 - x
6. (x+1)(x^2+x+1)
To expand this expression, we can use the distributive property. Multiply each term in the first parentheses by each term in the second parentheses and then combine like terms:
x * x^2 + x * x + x * 1 + 1 * x^2 + 1 * x + 1 * 1
This simplifies to: x^3 + x^2 + x^2 + x + x + 1
Combine the like terms: x^3 + 2x^2 + 2x + 1
So, the expansion is: x^3 + 2x^2 + 2x + 1
7. (x-1)(x^3+x^2+x)
Similarly, expand the expression by using the distributive property:
x * x^3 + x * x^2 + x * x + (-1) * x^3 + (-1) * x^2 + (-1) * x
This simplifies to: x^4 + x^3 + x^3 + x^2 + x^2 + x + (-x^3) + (-x^2) + (-x)
Combine the like terms: x^4 + x^3 + (-x^3) + x^2 + x^2 + (-x^2) + x + (-x)
Simplify further: x^4 + x
So, the expansion is: x^4 + x
I hope that helps! Let me know if you have any further questions.