factorization

Resolve in factors:

x⁴ – 10 x² + 9

Answer

Let x² = y

So, we have y² – 10y + 9

= y² – 9y – y + 9

= y(y – 9) – 1(y – 9)

= (y – 1)(y – 9)

= (x² – 1)( x²– 9)

=(x-1)(x +1)(x -9)(x +9)

Resolve into factors:

x² + 2xy + y² – x – y

Answer:

x² + 2xy + y² – x – y

= (x + y)² – (x – y)

=(x + y)(x + y – 1)

Resolve into factors:

 a(a+1) – b(b+ 1)

Answer:

= a² + a – b² – b

= (a – b)(a + b) +(a – b)

=(a – b) (a + b + 1)