IF YOU WANT IT STEP BY STEP HERE IT IS. HOPE YOU CAN FOLLOW IT.
Expand the following:
(x^2 (a+b^5) (a+b) (a-b^2))/8
Multiply a+b and a-b^2 together using FOIL.
(a+b) (a-b^2) = (a) (a) + (a) (-b^2) + (b) (a) + (b) (-b^2) = a^2-a b^2+a b-b^3 = a^2+a b-a b^2-b^3:
(x^2 a^2+a b-a b^2-b^3 (a+b^5))/8
Distribute a^2+a b-a b^2-b^3 over a+b^5.
(a^2+a b-a b^2-b^3) (a+b^5) = b^5 (a^2+a b-a b^2-b^3)+a (a^2+a b-a b^2-b^3):
(x^2 b^5 (a^2+a b-a b^2-b^3)+a (a^2+a b-a b^2-b^3))/8
Distribute b^5 over a^2+a b-a b^2-b^3.
b^5 (a^2+a b-a b^2-b^3) = b^5 a^2+b^5 a b+b^5 (-a b^2)+b^5 (-b^3):
(x^2 (b^5 a^2+b^5 a b-b^5 a b^2-b^5 b^3+a (a^2+a b-a b^2-b^3)))/8
Combine products of like terms.
b^5 a b = b^(5+1) a:
(x^2 (b^5 a^2+b^(5+1) a-b^5 a b^2-b^5 b^3+a (a^2+a b-a b^2-b^3)))/8
Evaluate 5+1.
5+1 = 6:
(x^2 (b^5 a^2+b^6 a-b^5 a b^2-b^5 b^3+a (a^2+a b-a b^2-b^3)))/8
Combine products of like terms.
b^5 (-a) b^2 = b^(5+2) (-a):
(x^2 (b^5 a^2+b^6 a+-(b^(5+2) a)-b^5 b^3+a (a^2+a b-a b^2-b^3)))/8
Evaluate 5+2.
5+2 = 7:
(x^2 (b^5 a^2+b^6 a-b^7 a-b^5 b^3+a (a^2+a b-a b^2-b^3)))/8
Combine products of like terms.
b^5 (-b^3) = b^(5+3) (-1):
(x^2 (b^5 a^2+b^6 a-b^7 a+-b^(5+3)+a (a^2+a b-a b^2-b^3)))/8
Evaluate 5+3.
5+3 = 8:
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a (a^2+a b-a b^2-b^3)))/8
Distribute a over a^2+a b-a b^2-b^3.
a (a^2+a b-a b^2-b^3) = a a^2+a a b+a (-a b^2)+a (-b^3):
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a a^2+a a b-a a b^2-a b^3))/8
Combine products of like terms.
a a^2 = a^(1+2):
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a^(1+2)+a a b-a a b^2-a b^3))/8
Evaluate 1+2.
1+2 = 3:
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a^3+a a b-a a b^2-a b^3))/8
Combine products of like terms.
a a b = a^2 b:
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a^3+a^2 b-a a b^2-a b^3))/8
Combine products of like terms.
a (-a) b^2 = -a^2 b^2:
(x^2 (b^5 a^2+b^6 a-b^7 a-b^8+a^3+a^2 b+-a^2 b^2-a b^3))/8
Distribute x^2 over a^3+a^2 b-a^2 b^2-a b^3+a^2 b^5+a b^6-a b^7-b^8.
x^2 (a^3+a^2 b-a^2 b^2-a b^3+a^2 b^5+a b^6-a b^7-b^8) = x^2 a^3+x^2 a^2 b+x^2 (-a^2 b^2)+x^2 (-a b^3)+x^2 a^2 b^5+x^2 a b^6+x^2 (-a b^7)+x^2 (-b^8):
x^2 a^3+x^2 a^2 b-x^2 a^2 b^2-x^2 a b^3+x^2 a^2 b^5+x^2 a b^6-x^2 a b^7-x^2 b^8/8
Express (a^3 x^2+a^2 b x^2-a^2 b^2 x^2-a b^3 x^2+a^2 b^5 x^2+a b^6 x^2-a b^7 x^2-b^8 x^2)/8 as a sum of fractions.
(a^3 x^2+a^2 b x^2-a^2 b^2 x^2-a b^3 x^2+a^2 b^5 x^2+a b^6 x^2-a b^7 x^2-b^8 x^2)/8 = (a^3 x^2)/8+(a^2 b x^2)/8-(a^2 b^2 x^2)/8-(a b^3 x^2)/8+(a^2 b^5 x^2)/8+(a b^6 x^2)/8-(a b^7 x^2)/8-(b^8 x^2)/8:
Answer: |
| (a^3 x^2)/8+(a^2 b x^2)/8-(a^2 b^2 x^2)/8-(a b^3 x^2)/8+(a^2 b^5 x^2)/8+(a b^6 x^2)/8-(a b^7 x^2)/8-(b^8 x^2)/8
