Question 1: Factorize each of the following expressions:
qr − pr + qs − ps
Answer 1: qr−pr+qs−ps
=(qr−pr)+(qs−ps) [Grouping the expressions]
=r(q−p)+s(q−p)
=(r+s)(q−p) [Taking (q−p) as the common factor]
Question 2: Factorize each of the following expressions:
p2q − pr2 − pq + r2
Answer 2: p2q−pr2−pq+r2
=(p2q−pq)+(r2−pr2) [Grouping the expressions]
=pq(p−1)+r2(1−p)
=pq(p−1)−r2(p−1) [∵(1−p)=−(p−1)]=(pq−r2)(p−1) [Taking (p−1) as the common factor]
Question 3: Factorize each of the following expressions:
1 + x + xy + x2y
Answer 3: 1+x+xy+x2y
=(1+x)+(xy+x2y) [Grouping the expressions]
=(1+x)+xy(1+x)
=(1+xy)(1+x) [Taking (1+x) as the common factor]
Question 4: Factorize each of the following expressions:
ax + ay − bx − by
Answer 4: ax+ay−bx−by
=(ax+ay)−(bx+by) [Grouping the expressions]
= a(x+y)−b(x+y)
= (a−b)(x+y) [Taking (x+y) as the common factor]
Question 5: Factorize each of the following expressions:
xa2 + xb2 − ya2 − yb2
Answer 5: xa2+xb2−ya2−y