Question

Factorise the following:

x² – x(3a + 2b) + 6ab

Answer 1

Given expression: x² – x(3a + 2b) + 6ab

Step-wise calculation:

Step 1: Expand the middle term:

x² – 3ax – 2bx + 6ab

Step 2: Rewrite the expression grouping terms to factor by grouping:

x² – 3ax – 2bx + 6ab = x² – 3ax – 2bx + 6ab

Step 3: Group terms:

(x² – 3ax) – (2bx – 6ab)

Step 4: Factor out common factors from each group:

x(x – 3a) – 2b(x – 3a)

Step 5: Factor out the common binomial factor:

(x – 3a)(x – 2b)

So, the factorization of the given expression is (x – 3a)(x – 2b).