HELP ME
Simplify each polynomial Write in standard form (Hint: watch for the operations, add, sub , multiply)
(6s^4+7s^2+7)+(8s^4-11s^2+9s)
(4h^3+3h+1)-(-5h^3+6h-2)
(8z^3-3z^2-7)-(z^3-z^2+9)
5k(3-4k)
4m(2m+9m^2-6)
q(11+8q-2q^2 )
(x-2)(x+4)
(6g+7)(3g-8)
(x-1)^2
(4y+2)^2
Please help me i dont have a lot of time
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will do one for you.
15k - 20k^2
I can help you with your polynomial simplification problems. Let's go step by step:
1. Simplify (6s^4+7s^2+7)+(8s^4-11s^2+9s):
To simplify this expression, combine like terms. Add the coefficients of the same degree terms.
6s^4 + 8s^4 = 14s^4
7s^2 - 11s^2 = -4s^2
Now, combine the remaining terms:
14s^4 - 4s^2 + 7s
The simplified expression in standard form is 14s^4 - 4s^2 + 7s.
2. Simplify (4h^3+3h+1)-(-5h^3+6h-2):
To simplify this expression, distribute the negative sign:
4h^3 + 3h + 1 + 5h^3 - 6h + 2
Combine like terms:
4h^3 + 5h^3 = 9h^3
3h - 6h = -3h
1 + 2 = 3
The simplified expression in standard form is 9h^3 - 3h + 3.
3. Simplify (8z^3-3z^2-7)-(z^3-z^2+9):
To simplify this expression, distribute the negative sign:
8z^3 - 3z^2 - 7 - z^3 + z^2 - 9
Combine like terms:
8z^3 - z^3 = 7z^3
-3z^2 + z^2 = -2z^2
-7 - 9 = -16
The simplified expression in standard form is 7z^3 - 2z^2 - 16.
4. Simplify 5k(3-4k):
To simplify this expression, distribute the 5k:
5k * 3 - 5k * 4k
Multiply:
15k - 20k^2
The simplified expression in standard form is -20k^2 + 15k.
5. Simplify 4m(2m+9m^2-6):
To simplify this expression, distribute the 4m:
4m * 2m + 4m * 9m^2 - 4m * 6
Multiply:
8m^2 + 36m^3 - 24m
The simplified expression in standard form is 36m^3 + 8m^2 - 24m.
6. Simplify q(11+8q-2q^2):
To simplify this expression, distribute the letter q:
q * 11 + q * 8q - q * 2q^2
Multiply:
11q + 8q^2 - 2q^3
The simplified expression in standard form is -2q^3 + 8q^2 + 11q.
7. Simplify (x-2)(x+4):
To simplify this expression, use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms:
(x * x) + (x * 4) + (-2 * x) + (-2 * 4)
Simplify each term:
x^2 + 4x - 2x - 8
Combine like terms:
x^2 + 2x - 8
The simplified expression in standard form is x^2 + 2x - 8.
8. Simplify (6g+7)(3g-8):
To simplify this expression, use the FOIL method:
(6g * 3g) + (6g * -8) + (7 * 3g) + (7 * -8)
Simplify each term:
18g^2 - 48g + 21g - 56
Combine like terms:
18g^2 - 27g - 56
The simplified expression in standard form is 18g^2 - 27g - 56.
9. Simplify (x-1)^2:
To simplify this expression, use the formula for squaring a binomial:
(x - 1)^2 = (x - 1)(x - 1)
Use the FOIL method:
(x * x) + (x * -1) + (-1 * x) + (-1 * -1)
Simplify each term:
x^2 - x - x + 1
Combine like terms:
x^2 - 2x + 1
The simplified expression in standard form is x^2 - 2x + 1.
10. Simplify (4y+2)^2:
To simplify this expression, use the formula for squaring a binomial:
(4y + 2)^2 = (4y + 2)(4y + 2)
Use the FOIL method:
(4y * 4y) + (4y * 2) + (2 * 4y) + (2 * 2)
Simplify each term:
16y^2 + 8y + 8y + 4
Combine like terms:
16y^2 + 16y + 4
The simplified expression in standard form is 16y^2 + 16y + 4.
To simplify each polynomial and write them in standard form, we need to perform the operations indicated (addition, subtraction, and multiplication) and combine like terms. Let's go through each problem step-by-step:
1. (6s^4+7s^2+7) + (8s^4-11s^2+9s)
To simplify this expression, we need to combine the like terms by adding or subtracting them. Notice that the terms with the same variable and exponent can be combined.
So, (6s^4+8s^4) + (7s^2-11s^2) + (7+9s)
= 14s^4 - 4s^2 + 9s + 7
Therefore, the simplified form in standard form is 14s^4 - 4s^2 + 9s + 7.
2. (4h^3+3h+1) - (-5h^3+6h-2)
To simplify this expression, we need to distribute the negative sign to all the terms inside the parentheses after removing the parentheses.
So, (4h^3+3h+1) + (5h^3-6h+2)
= 4h^3 + 5h^3 + 3h - 6h + 1 + 2
= 9h^3 - 3h + 3
Therefore, the simplified form in standard form is 9h^3 - 3h + 3.
3. (8z^3-3z^2-7) - (z^3-z^2+9)
To simplify this expression, we need to distribute the negative sign to all the terms inside the parentheses after removing the parentheses.
So, (8z^3-3z^2-7) - z^3 + z^2 - 9
= 8z^3 - z^3 - 3z^2 + z^2 - 7 - 9
= 7z^3 - 2z^2 - 16
Therefore, the simplified form in standard form is 7z^3 - 2z^2 - 16.
4. 5k(3-4k)
To simplify this expression, we need to distribute the 5k to both terms inside the parentheses.
So, 5k * 3 - 5k * 4k
= 15k - 20k^2
Therefore, the simplified form in standard form is -20k^2 + 15k.
5. 4m(2m+9m^2-6)
To simplify this expression, we need to distribute the 4m to all three terms inside the parentheses.
So, 4m * 2m + 4m * 9m^2 - 4m * 6
= 8m^2 + 36m^3 - 24m
Therefore, the simplified form in standard form is 36m^3 + 8m^2 - 24m.
6. q(11+8q-2q^2)
To simplify this expression, we need to distribute the q to all three terms inside the parentheses.
So, q * 11 + q * 8q - q * 2q^2
= 11q + 8q^2 - 2q^3
Therefore, the simplified form in standard form is -2q^3 + 8q^2 + 11q.
7. (x-2)(x+4)
To simplify this expression, we need to use the distributive property by multiplying each term in the first parenthesis by each term in the second parenthesis.
So, (x * x) + (x * 4) + (-2 * x) + (-2 * 4)
= x^2 + 4x - 2x - 8
= x^2 + 2x - 8
Therefore, the simplified form in standard form is x^2 + 2x - 8.
8. (6g+7)(3g-8)
Using the distributive property, we multiply each term in the first parenthesis by each term in the second parenthesis.
So, (6g * 3g) + (6g * -8) + (7 * 3g) + (7 * -8)
= 18g^2 - 48g + 21g - 56
= 18g^2 - 27g - 56
Therefore, the simplified form in standard form is 18g^2 - 27g - 56.
9. (x-1)^2
To simplify this expression, we need to square the binomial using the formula (a-b)^2 = a^2 - 2ab + b^2.
So, (x-1)^2 = x^2 - 2(x)(1) + 1^2
= x^2 - 2x + 1
Therefore, the simplified form in standard form is x^2 - 2x + 1.
10. (4y+2)^2
Similar to the previous question, we need to square the binomial using the formula (a+b)^2 = a^2 + 2ab + b^2.
So, (4y+2)^2 = (4y)^2 + 2(4y)(2) + 2^2
= 16y^2 + 16y + 4
Therefore, the simplified form in standard form is 16y^2 + 16y + 4.
I hope this helps! If you have any further questions, feel free to ask.