Question

Factorize the following
a.3pq – ps – 12rq + 4rs
b.4^2- 8x + 3
c.(−3) ^2 - 4^2

Answer 1

a. Factorize 3pq - ps - 12rq + 4rs as (q - s)(3p - 4r). b. Factorize
`4^2 - 8x + 3` as (2x - 1)(2x - 3). c. Factorize
`(-3)^2 - 4^2` as (-1)(7).

Step-by-step explanation:

a. To factorize 3pq - ps - 12rq + 4rs, we can group the terms and factor out common factors from each group. This gives us p(3q - s) - 4r(q - s).

Now, we can factor out a common factor of (q - s) from both terms, resulting in (q - s)(3p - 4r).

b. The expression
`4^2 - 8x + 3` can be factored as (2x - 1)(2x - 3).

c. Similarly,
`(-3)^2 - 4^2` can be factored as (3 - 4)(3 + 4), which simplifies to (-1)(7).