Maths help please!!?

Question

i need help in these 3 questions i dont undertand how to answer them

1.x^6-y^6

2.a^3-b^3-a+b

3.ab(x^2 +y^2) - xy(a^2+b^2)

Answer 1

Simplify or factor?

1.x^6-y^6 ← Difference of two squares

(x³ + y³)(x³ - y³) ← These are each the sum/difference of two cubes.

(x + y)(x² - xy + y²)(x - y)(x² + xy + y²)

2.a^3-b^3-a+b

(a³ - b³) is the difference of two cubes

(a - b)(a² + ab + b²) - a + b

-1(b - a)(a² + ab + b²) + (b - a)

(b - a)(-a² - ab - b²) + (b - a)

(b - a)(-a² - ab - b² + 1)

3.ab(x^2 +y^2) - xy(a^2+b^2)

Distribute:

(abx² + aby²) - (a²xy + b²xy)

abx² + aby² - a²xy - b²xy

Rearrange:

abx² - a²xy + aby² - b²xy

Factor by grouping:

ax(bx - ay) + by(ay - bx)

-ax(ay - bx) + by(ay - bx)

(ay - bx)(by - ax)