Pls help me!!
I need the answers to these few questions I just cant figure them out and I have to turn them in asap
Simplify each polynomial. Write each in standard form.
HINT: Watch for the operation! Add? Subtract? Or Multiply?
8. 4m(2m+9m^2-6)
9. q(11+8q-2q^2 )
10. (x-2)(x+4)
11. (6g+7)(3g-8)
12. (x-1)^2
13. (4y+2)^2
Want to see your attempts to see what the problem is. I will do one two ways as an example:
10. (x-2)(x+4)
This can be written as
x(x+4) -2 (x+4)
= x^2 + 4x - 2x - 8
= x^2 + 2x - 8
OR
use FOIL (first outer inner last)
x^2- 4x - 2x - 8 which is a similar ressult
Sure! I can help you simplify these polynomials.
Let's start with question 8:
8. 4m(2m+9m^2-6)
To simplify this polynomial, we need to perform the multiplication by distributing the 4m to each term inside the parentheses.
4m * 2m = 8m^2
4m * 9m^2 = 36m^3
4m * -6 = -24m
So, the simplified expression is:
8m^2 + 36m^3 - 24m
Now, let's move on to question 9:
9. q(11+8q-2q^2)
Again, we'll distribute the q to each term inside the parentheses.
q * 11 = 11q
q * 8q = 8q^2
q * -2q^2 = -2q^3
Therefore, the simplified expression is:
11q + 8q^2 - 2q^3
Next, question 10:
10. (x-2)(x+4)
To simplify this polynomial, we can use the distributive property. Multiply each term inside the first parentheses by each term inside the second parentheses.
(x * x) + (x * 4) + (-2 * x) + (-2 * 4)
= x^2 + 4x - 2x - 8
Combining like terms, we get:
x^2 + 2x - 8
Moving on to question 11:
11. (6g+7)(3g-8)
Apply the distributive property again:
(6g * 3g) + (6g * -8) + (7 * 3g) + (7 * -8)
= 18g^2 - 48g + 21g - 56
Combining like terms gives us:
18g^2 - 27g - 56
For question 12:
12. (x-1)^2
This is an example of squaring a binomial. We can use the formula for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2.
In this case, a = x and b = 1. So, plugging in the values, we get:
(x - 1)^2 = x^2 - 2(x)(1) + 1
Simplifying further, we have:
x^2 - 2x + 1
Finally, question 13:
13. (4y+2)^2
Similar to question 12, this is another example of squaring a binomial.
Using the formula (a + b)^2 = a^2 + 2ab + b^2, with a = 4y and b = 2:
(4y + 2)^2 = (4y)^2 + 2(4y)(2) + (2)^2
= 16y^2 + 16y + 4
So, the simplified expression is:
16y^2 + 16y + 4.
I hope that helps! Let me know if you have any other questions.