Final answer:
For expression (a), 3p² + 6p is factorized as 3p(p + 2). For expression (b), 4q² - 1 is a difference of squares and factorizes to (2q - 1)(2q + 1).
Step-by-step explanation:
The student has asked to factorize completely the following expressions: (a) 3p² + 6p and (b) 4q² - 1.
Factorization of 3p² + 6p
First, we identify a common factor in both terms of the expression. The common factor is 3p:
3p² + 6p = 3p(p + 2)
This expression cannot be factored further, so 3p(p + 2) is the completely factorized form of 3p² + 6p.
Factorization of 4q² - 1
The expression 4q² - 1 is a difference of squares and can be factored into:
4q² - 1 = (2q - 1)(2q + 1)
The factorization is now complete.
In answering similar questions, we should eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.