3. Example 1. Factor 2a2 + ab + b2 + 2ab.
= 2a2 + ab + b2 + 2ab
= (2a2 + ab) + (2ab + b2) -Group the terms with common factor
= a(2a + b) + b(2a + b) -Factor out the common binomial factor
= (2a + b)(a + b) -Factor
Thus, the factored form of 2a2 + ab + b2 + 2ab is (2a + b)(a + b).
4. Example 2. Factor 2x2 + xy + 2xy + y2 .
= 2x2 + xy + 2xy + y2
= (2x2 + xy) + (2xy + y2) - Group the terms that has a common
factor
= x(2x + y) + y(2x + y) - Factor out the common binomial factor
= (2x + y) (x + y) - Factor
Thus, the factored form is (2x + y)(x + y).
5. Example 3. Factor 3a2b – 2a + 9ab – 6.
= (3a2b – 2a + 9ab - 6
= (3a2b – 2a) + (9ab – 6) -Group the terms with common factor
= a(3ab – 2) + 3(3ab – 2) -Factor out the common binomial factor
= (a + 3)(3ab – 2) -Factor
Thus, the factored form is (a + 3)(3ab – 2).
6. Example 4. Factor 2m2 – n2 – mn + 2mn.
= 2m2 – n2 – mn + 2mn
= (2m2 – mn) + (2mn – n2) -Group the terms with common factor)
= m(2m – n) + n(2m – n) -Factor out the common binomial factor
= (m + n)(2m – n) -Factor
Thus, the factored form is (m + n)(2m – n).
7. Example 5. Factor 3x2 – 2x + 4 – 6x.
= 3x2 – 2x + 4 – 6x
= (3x2 – 6x) – (2x + 4) -Group the terms with common factor
= 3x(x – 2) -2(x - 2) -Factor out the common binomial factor
= (x – 2)(3x – 2) -Factor
Thus, the factored form is (x – 2)(3x - 2).
