RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-6) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Class 8: RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-6) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The document RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-6) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
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Question 1: Factorize each of the following algebraic expression:
4x2 + 12xy +9y2
Answer 1: 4x2+12xy+9y2 

=(2x)2+2×2x×3y+(3y)2 
=(2x+3y)2 
=(2x+3y)(2x+3y) 
Question 2: Factorize each of the following algebraic expression:
9a2 − 24ab + 16b2
Answer 2: 9a224ab+16b2 

=(3a)22×3a×4b+(4b)2 
=(3a4b)2 
=(3a4b)(3a4b) 
Question 3: Factorize each of the following algebraic expression:
p2q2 − 6pqr + 9r2
Answer 3:
p2q2−6pqr+9r2 
=(pq)22×pq×3r+(3r)2 
=(pq3r)2 
=(pq3r)(pq3r) 
Question 4: Factorize each of the following algebraic expression:
36a2 + 36a + 9
Answer 4: 36a2+36a+9 

=9(4a2+4a+1) 
=9{(2a)2+2×2a×1+12} 
=9(2a+1)2 
=9(2a+1)(2a+1) 
Question 5: Factorize each of the following algebraic expression:
a2 + 2ab + b2 − 16
Answer 5: a2+2ab+b216 

=a2+2×a×b+b216 
=(a+b)242 
=(a+b4)(a+b+4) 
Question 6: Factorize each of the following algebraic expression:
9z2x2 + 4xy − 4y2
Answer 6: 9z2x2+4xy4y2 

=9z2(x24xy+4y2) 
=9z2[x22×x×2y+(2y)2] 
=(3z)2(x2y)2 
=[3z−(x−2y)][3z+(x−2y)]
=(3zx+2y)(3z+x2y)=(x2y+3z)(x+2y+3z)
Question 7: Factorize each of the following algebraic expression:
9a4 − 24a2b2 + 16b4 − 256
Answer 7: 9a424a2b2+16b4256 

=(9a424a2b2+16b4)256 
=[(3a2)22×3a2×4b2+(4b2)2]162 
=(3a24b2)2162 
=[(3a24b2)16][(3a24b2)+16] 
=(3a24b216)(3a24b2+16) 
Question 8: Factorize each of the following algebraic expression:
16 − a6 + 4a3b3 − 4b6
Answer 8: 16a6+4a3b34b6 

=16(a64a3b3+4b6) 
=42[(a3)22×a3×2b3+(2b3)2] 
=42(a32b3)2 
=[4(a32b3)][4+(a32b3)] 
=(4a3+2b3)(4+a32b3) 
=(a32b3+4)(a3+2b3+4) 
Question 9: Factorize each of the following algebraic expression:
a2 − 2ab + b2c2
Answer 9: a22ab+b2c2 

=(a22ab+b2)c2 
=(a22×a×b+b2)c2 
=(ab)2c2 
=[(ab)c][(ab)+c] 
=(abc)(ab+c)
Question 10: Factorize each of the following algebraic expression:
x2 + 2x + 1 − 9y2
Answer 10:
x2+2x+19y2 
=(x2+2x+1)9y2 
=(x2+2×x×1+1)9y2 
=(x+1)2(3y)2 
=[(x+1)3y][(x+1)+3y] 
=(x+13y)(x+1+3y) 
=(x+3y+1)(x3y+1) 
Question 11: Factorize each of the following algebraic expression:
a2 + 4ab + 3b2
Answer 11: a2+4ab+3b2 

=a2+4ab+4b2b2 
=[a2+2×a×2b+(2b)2]b2 
=(a+2b)2b2 
=[(a+2b)b][(a+2b)+b] 
=(a+2bb)(a+2b+b) 
=(a+b)(a+3b) 
Question 12: Factorize each of the following algebraic expression:
96 − 4xx2
Answer 12: 964xx2 

=10044xx2 
=100(x2+4x+4) 
=100(x2+2×x×2+22) 
=102(x+2)2 
=[10(x+2)][10+(x+2)] 
=(10x2)(10+x+2) 
=(8x)(12+x) 
=(x+12)(x+8) 
Question 13: Factorize each of the following algebraic expression:
a4 + 3a2 +4
Answer 13: a4+3a2+4 

=a4+4a2a2+4 
=(a4+4a2+4)a2 
=[(a2)2+2×a2×2+22]a2 
=(a2+2)2a2 
=[(a2+2)a][(a2+2)+a] 
=(a2a+2)((a2+a+2) 
Question 14: Factorize each of the following algebraic expression:
4x4 + 1

Answer 14:
4x4+1
=4x4+4x2+14x2 
=[(2x2)2+2×2x2×1+1]4x2 
=(2x2+1)2(2x)2 
=[(2x2+1)2x][(2x2+1)+2x] 
=(2x22x+1)(2x2+2x+1) 
Question 15: Factorize each of the following algebraic expression:
4x4 + y

Answer 15: 4x4+y4 
=4x4+4x2y2+y44x2y2 
=[(2x2)2+2×2x2×y+(y2)2](2xy)2 
=(2x2+y2)2(2xy)2 
=[(2x2+y2)2xy][(2x2+y2)+2xy] 
=(2x22xy+y2)(2x2+2xy+y2) 
Question 16: Factorize each of the following algebraic expression:
(x + 2)2 − 6(x + 2) + 9
Answer 16: (x+2)26(x+2)+9 

=(x+2)22×(x+2)×3+32 
=[(x+2)3]2 
=(x+23)2 
=(x1)2 
=(x1)(x1)
Question 17: Factorize each of the following algebraic expression:
25 − p2q2 − 2pq
Answer 17: 25p2q22pq 

=25(p2+2pq+q2) 
=52(p2+2×p×q+q2) 
=52(p+q)2 
=[5(p+q)][5+(p+q)] 
=(5pq)(5+p+q) 
=(p+q5)(p+q+5) 
Question 18: Factorize each of the following algebraic expression:
x2 + 9y2 − 6xy − 25a2
Answer 18:
 x
2
+9y26xy25a2 

=(x26xy+9y2)25a2 
=[x22×x×3y+(3y)2]25a2 
=(x3y)2(5a)2 
=[(x3y)5a][(x3y)+5a] 
=(x3y5a)(x3y+5a) 
Question 19: Factorize each of the following algebraic expression:
49 − a2 + 8ab − 16b2
Answer 19: 49a2+8ab16b2 

=49(a28ab+16b2) 
=49[a22×a×4b+(4b)2] 
=72(a4b)2 
=[7(a4b)][7+(a4b)] 
=(7a+4b)(7+a4b) 
=(a4b7)(a4b+7) 
=(a4b+7)(a4b7) 
Question 20: Factorize each of the following algebraic expression:
a2 − 8ab + 16b2 − 25c2
Answer 20: a28ab+16b225c2 

=(a28ab+16b2)25c2 
=[a22×a×4b+(4b)2]25c2 
=(a4b)2(5c)2 
=[(a4b)5c][(a4b)+5c] 
=(a4b5c)(a4b+5c) 
Question 21: Factorize each of the following algebraic expression:
x2y2 + 6y − 9
Answer 21: x2y2+6y9 

=x2(y26y+9) 
=x2(y22×y×3+32) 
=x2(y3)2 
=[x(y3)][