Question 8 of 17intermediate🔧 ApplyNumerical6 marks
Simplify each of the following expressions:
(a)
p + p + p + p, p + p + p + q
Answer
p + p + p + p = 4p; p + p + p + q = 3p + q
(b)
p - q + p - q
Answer
2p - 2q
(c)
p + q - (p + q)
Answer
0
(d)
2d - d - d - d
Answer
-d
(e)
2d - d - (d - c)
Answer
c
(f)
2d - d - c - c
Answer
d - 2c
Explanation
(a) Like terms can be combined. In the first expression, all terms are p, giving 4p. In the second, p terms combine to 3p, and q remains separate. (b) Group like terms: (p + p) + (-q - q) = 2p - 2q (c) Remove brackets: p + q - p - q = (p - p) + (q - q) = 0 (d) 2d - d - d - d = (2d - d) - d - d = d - d - d = -d (e) 2d - d - (d - c) = d - d + c = c (f) 2d - d - c - c = d - 2c