Given:
Polynomials: ![a+3 \text { and }-2 a^{2}+15 a+6 b^{2}](https://tex.z-dn.net/?f=a%2B3%20%5Ctext%20%7B%20and%20%7D-2%20a%5E%7B2%7D%2B15%20a%2B6%20b%5E%7B2%7D)
To find:
The product of the polynomials.
Solution:
![(a+3)(-2 a^{2}+15 a+6 b^{2})](https://tex.z-dn.net/?f=%28a%2B3%29%28-2%20a%5E%7B2%7D%2B15%20a%2B6%20b%5E%7B2%7D%29)
Using distributive property: ![x(y+z)=xy+xz](https://tex.z-dn.net/?f=x%28y%2Bz%29%3Dxy%2Bxz)
![(a+3)(-2 a^{2}+15 a+6 b^{2})=a(-2 a^{2}+15 a+6 b^{2})+3(-2 a^{2}+15 a+6 b^{2})](https://tex.z-dn.net/?f=%28a%2B3%29%28-2%20a%5E%7B2%7D%2B15%20a%2B6%20b%5E%7B2%7D%29%3Da%28-2%20a%5E%7B2%7D%2B15%20a%2B6%20b%5E%7B2%7D%29%2B3%28-2%20a%5E%7B2%7D%2B15%20a%2B6%20b%5E%7B2%7D%29)
Now multiply each of the first term with each of the second term.
![=a\left(-2 a^{2}\right)+a \cdot 15 a+a \cdot 6 b^{2}+3\left(-2 a^{2}\right)+3 \cdot 15 a+3 \cdot 6 b^{2}](https://tex.z-dn.net/?f=%3Da%5Cleft%28-2%20a%5E%7B2%7D%5Cright%29%2Ba%20%5Ccdot%2015%20a%2Ba%20%5Ccdot%206%20b%5E%7B2%7D%2B3%5Cleft%28-2%20a%5E%7B2%7D%5Cright%29%2B3%20%5Ccdot%2015%20a%2B3%20%5Ccdot%206%20b%5E%7B2%7D)
Applying plus minus rule: ![+(-x)=-x](https://tex.z-dn.net/?f=%2B%28-x%29%3D-x)
![=-2 a^{2} \cdot a+15 a \cdot a+6 a\cdot b^{2}-3 \cdot 2 a^{2}+3 \cdot 15 a+3 \cdot 6 b^{2}](https://tex.z-dn.net/?f=%3D-2%20a%5E%7B2%7D%20%5Ccdot%20a%2B15%20a%20%5Ccdot%20a%2B6%20a%5Ccdot%20%20b%5E%7B2%7D-3%20%5Ccdot%202%20a%5E%7B2%7D%2B3%20%5Ccdot%2015%20a%2B3%20%5Ccdot%206%20b%5E%7B2%7D)
Apply the exponent rule: ![x^{n} \cdot x^{m}=x^{n+m}](https://tex.z-dn.net/?f=x%5E%7Bn%7D%20%5Ccdot%20x%5E%7Bm%7D%3Dx%5E%7Bn%2Bm%7D)
![=-2 a^{3}+15 a^2+6 a b^{2}-6 a^{2}+45 a+18 b^{2}](https://tex.z-dn.net/?f=%3D-2%20a%5E%7B3%7D%2B15%20a%5E2%2B6%20a%20%20b%5E%7B2%7D-6%20a%5E%7B2%7D%2B45%20a%2B18%20b%5E%7B2%7D)
Add or subtract the like terms:
![=-2 a^{3}+15 a^2-6a^2+6 a b^{2}+45 a+18 b^{2}](https://tex.z-dn.net/?f=%3D-2%20a%5E%7B3%7D%2B15%20a%5E2-6a%5E2%2B6%20a%20%20b%5E%7B2%7D%2B45%20a%2B18%20b%5E%7B2%7D)
![=-2 a^{3}+9 a^{2}+6 a b^{2}+45 a+18 b^{2}](https://tex.z-dn.net/?f=%3D-2%20a%5E%7B3%7D%2B9%20a%5E%7B2%7D%2B6%20a%20b%5E%7B2%7D%2B45%20a%2B18%20b%5E%7B2%7D)
Arrange in the order.
![=-2 a^{3}+9 a^{2}+45 a+6 a b^{2}+18 b^{2}](https://tex.z-dn.net/?f=%3D-2%20a%5E%7B3%7D%2B9%20a%5E%7B2%7D%2B45%20a%2B6%20a%20b%5E%7B2%7D%2B18%20b%5E%7B2%7D)
The product of
.
Answer:
mass in grams /over/ volume in cubic centimeters!
Step-by-step explanation:
Answer:highlight or put quotes around certain verbs like "chop" or "simmer"
Step-by-step explanation:
Answer:
Step-by-step explanation:
Givens
y2 = - 4
y1 = - 8
x2 = - 3
x1 = - 2
==========
Equation
m = (y2 - y1) / (x2 - x1)
m = (-4 - - 8) / (-3 - - 2)
m = 4 / - 1
m = - 4