Can you please help me factor the following polynomials..?

Question

1) a^6 - b^6

2) 11a^2 - ab - 21b^2

Thanks.

Answer 1

Difference of squares (x^2-y^2) factors to (x+y)(x-y) For the first problem try figuring out what x and y might be.

For the second problem let's complete the square... Adding (1/22)^2 b^2 gives us.

11a^2 - ab + (1/22)^2b^2 -21b^2 -(1/22)^2b^2

(sqrt 11 a - 1/22)^2 = (21+(1/22)^2)b^2

Sqrt each side

sqrt 11a - 1/22 = Pos and Neg sqrt (21 + (1/22)^2)b

Solve for sqrt 11a and then each solution gets a parenthesis

(sqrt 11 a + stuff) (sqrt 11 a - stuff) = factored