RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-4) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

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