Answer:
(i) xy² +xy +y +1 can be factorized by grouping:
xy² + xy + y + 1
= xy(x + y) + 1(x + y)
= (xy + 1)(x + y)
Therefore, xy² +xy +y +1 = (xy + 1)(x + y).
(ii) x² -7x +12 can be factorized by finding two numbers that multiply to 12 and add up to -7. These numbers are -4 and -3, so we can write:
x² - 7x + 12 = (x - 4)(x - 3)
Therefore, x² -7x +12 = (x - 4)(x - 3).
(iii) x² - 144 is a difference of squares, and can be factorized as:
x² - 144 = (x + 12)(x - 12)
Therefore, x² - 144 = (x + 12)(x - 12).