Harder Factorise

Algebra – Harder Factorise or Factoring can be done by collecting common factors and using sums and products of factors.
$$x^2 – (a+b)x + ab = (x-a)(x-b)$$

Question 1

Factorise \( (x^2-3x)^2 -2x^2 + 6x – 8 \).

Question 2

Factorise \( (x-1)(x-3)(x+2)(x+4) + 24 \).

Question 3

Factorise \( x^4 – 5x^2 +4 \).

Question 4

Factorise \( x^4 + x^2 + 1 \).

Question 5

Factorise \( x^4 – 6x^2y^2 + y^4 \).

Question 6

Factorise \( x^3 + 2x^2y^2 – x – 2y \).

Question 7

Factorise \( x^3 + x^2z + xz^2 – y^3 – y^2z – yz^2 \).

Question 8

Factorise \( (x^2 – 8x + 12)(x^2 – 7x + 12) – 6x^2 \).