Simplification

Question 1

(a+b)^2

Answer 1

a^2 + b^2 + 2ab

Question 2

(a-b)^2

Answer 2

a^2 + b^2 - 2ab.

Question 3

(a+b)^2 + (a-b)^2

Answer 3

2(a^2 + b^2)

Question 4

(a+b)^2 - (a-b)^2

Answer 4

4ab

Question 5

(a^2 - b^2)

Answer 5

(a+b)(a-b)

Question 6

(a+b)^3

Answer 6

a^3 + b^3 + 3ab(a+b)

Question 7

(a-b)3

Answer 7

a^3 - b^3 - 3ab(a-b)

Question 8

(a^3 + b^3)

Answer 8

(a+b)(a^2 - ab + b^2)

Question 9

a^3 - b^3

Answer 9

(a-b)(a^2 + ab + b^2)

Question 10

(a+b+c)^2

Answer 10

a^2 + b^2 + c^2 + 2(ab + bc + ca)

Question 11

a^3 + b^3 + c^3 - 3abc

Answer 11

(a+b+c)(a^2 + b^2 + c^2 -ab -bc - ca)

Question 12

n(A-B) + n(A intersection B)

Answer 12

n(A)

Question 13

n(B-A) + n(A intersection B)

Answer 13

n(B)

Question 14

n(A union B)

Answer 14

n(A-B) + n(A intersection B) + n(B-A)

Question 15

n(A union B)

Answer 15

n(A) + n(B) - n(A intersection B)