To simplify the given expression, we will first expand and simplify each term within the expression.
Expand (a+1)(a^2-b^2)(a+1)(a^2-b^2= a(a^2-b^2) + 1(a^2-b^2= a^3 - ab^2 + a^2 - b^2
Expand (a+b)(a^2-1)(a+b)(a^2-1= a(a^2-1) + b(a^2-1= a^3 - a + ba^2 - b
Now, put the simplified terms together:
(a^3 - ab^2 + a^2 - b^2) - (a^3 - a + ba^2 - b= a^3 - ab^2 + a^2 - b^2 - a^3 + a - ba^2 + = a^2 - ab^2 + a - b^2 - a + b - ba^= a^2 - ab^2 + a - b^2 - a + b - ba^= a^2 - 2ab^2 + b
Therefore, (a+1)(a^2-b^2)-(a+b)(a^2-1) simplifies to: a^2 - 2ab^2 + b.
To simplify the given expression, we will first expand and simplify each term within the expression.
Expand (a+1)(a^2-b^2)
(a+1)(a^2-b^2
= a(a^2-b^2) + 1(a^2-b^2
= a^3 - ab^2 + a^2 - b^2
Expand (a+b)(a^2-1)
(a+b)(a^2-1
= a(a^2-1) + b(a^2-1
= a^3 - a + ba^2 - b
Now, put the simplified terms together:
(a^3 - ab^2 + a^2 - b^2) - (a^3 - a + ba^2 - b
= a^3 - ab^2 + a^2 - b^2 - a^3 + a - ba^2 +
= a^2 - ab^2 + a - b^2 - a + b - ba^
= a^2 - ab^2 + a - b^2 - a + b - ba^
= a^2 - 2ab^2 + b
Therefore, (a+1)(a^2-b^2)-(a+b)(a^2-1) simplifies to: a^2 - 2ab^2 + b.