Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Factorization - Exercise 7.6
Factorization - Exercise 7.6 | Mathematics (Maths) Class 8 PDF Download
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Page 1
Q u e s t i o n : 1 2 0
Factorize each of the following algebraic expression:
4x
2
+ 12xy +9y
2
S o l u t i o n :
4x2+12xy+9y2=(2x)2+2×2x×3y+(3y)2=(2x+3y)2=(2x+3y)(2x+3y)
Q u e s t i o n : 1 2 1
Factorize each of the following algebraic expression:
9a
2
- 24ab + 16b
2
S o l u t i o n :
9a2-24ab+16b2=(3a)2-2×3a×4b+(4b)2=(3a-4b)2=(3a-4b)(3a-4b)
Q u e s t i o n : 1 2 2
Factorize each of the following algebraic expression:
p
2
q
2
- 6pqr + 9r
2
S o l u t i o n :
p2q2-6pqr+9r2=(pq)2-2×pq×3r+(3r)2=(pq-3r)2=(pq-3r)(pq-3r)
Q u e s t i o n : 1 2 3
Factorize each of the following algebraic expression:
36a
2
+ 36a + 9
S o l u t i o n :
36a2+36a+9=9(4a2+4a+1)=9(2a)2+2×2a×1+12=9(2a+1)2=9(2a+1)(2a+1)
Q u e s t i o n : 1 2 4
Factorize each of the following algebraic expression:
a
2
+ 2ab + b
2
- 16
S o l u t i o n :
a2+2ab+b2-16=a2+2×a×b+b2-16=(a+b)2-42=(a+b-4)(a+b+4)
Q u e s t i o n : 1 2 5
Factorize each of the following algebraic expression:
9z
2
- x
2
+ 4xy - 4y
2
S o l u t i o n :
9z2-x2+4xy-4y2=9z2-(x2-4xy+4y2)=9z2-[x2-2×x×2y+(2y)2]=(3z)2-(x-2y)2=[3z-(x-2y)][3z+(x-2y)]=(3z-x+2y)(3z+x-2y)=(x-2y+3z)(-x+2y+3z)
Q u e s t i o n : 1 2 6
Factorize each of the following algebraic expression:
9a
4
- 24a
2
b
2
+ 16b
4
- 256
S o l u t i o n :
9a4-24a2b2+16b4-256=(9a4-24a2b2+16b4)-256=[(3a2)2-2×3a2×4b2+(4b2)2]-162=(3a2-4b2)2-162=[(3a2-4b2)-16][(3a2-4b2)+16]=(3a2-4b2-16)(3a2-4b2+16)
Q u e s t i o n : 1 2 7
Factorize each of the following algebraic expression:
16 - a
6
+ 4a
3
b
3
- 4b
6
S o l u t i o n :
16-a6+4a3b3-4b6=16-(a6-4a3b3+4b6)=42-[(a3)2-2×a3×2b3+(2b3)2]=42-(a3-2b3)2=[4-(a3-2b3)][4+(a3-2b3)]=(4-a3+2b3)(4+a3-2b3)=(a3-2b3+4)(-a3+2b3+4)
Q u e s t i o n : 1 2 8
Factorize each of the following algebraic expression:
a
2
- 2ab + b
2
- c
2
S o l u t i o n :
a2-2ab+b2-c2=(a2-2ab+b2)-c2=(a2-2×a×b+b2)-c2=(a-b)2-c2=[(a-b)-c][(a-b)+c]=(a-b-c)(a-b+c)
Q u e s t i o n : 1 2 9
Factorize each of the following algebraic expression:
x
2
+ 2x + 1 - 9y
2
S o l u t i o n :
x2+2x+1-9y2=(x2+2x+1)-9y2=(x2+2×x×1+1)-9y2=(x+1)2-(3y)2=[(x+1)-3y][(x+1)+3y]=(x+1-3y)(x+1+3y)=(x+3y+1)(x-3y+1)
Page 2
Q u e s t i o n : 1 2 0
Factorize each of the following algebraic expression:
4x
2
+ 12xy +9y
2
S o l u t i o n :
4x2+12xy+9y2=(2x)2+2×2x×3y+(3y)2=(2x+3y)2=(2x+3y)(2x+3y)
Q u e s t i o n : 1 2 1
Factorize each of the following algebraic expression:
9a
2
- 24ab + 16b
2
S o l u t i o n :
9a2-24ab+16b2=(3a)2-2×3a×4b+(4b)2=(3a-4b)2=(3a-4b)(3a-4b)
Q u e s t i o n : 1 2 2
Factorize each of the following algebraic expression:
p
2
q
2
- 6pqr + 9r
2
S o l u t i o n :
p2q2-6pqr+9r2=(pq)2-2×pq×3r+(3r)2=(pq-3r)2=(pq-3r)(pq-3r)
Q u e s t i o n : 1 2 3
Factorize each of the following algebraic expression:
36a
2
+ 36a + 9
S o l u t i o n :
36a2+36a+9=9(4a2+4a+1)=9(2a)2+2×2a×1+12=9(2a+1)2=9(2a+1)(2a+1)
Q u e s t i o n : 1 2 4
Factorize each of the following algebraic expression:
a
2
+ 2ab + b
2
- 16
S o l u t i o n :
a2+2ab+b2-16=a2+2×a×b+b2-16=(a+b)2-42=(a+b-4)(a+b+4)
Q u e s t i o n : 1 2 5
Factorize each of the following algebraic expression:
9z
2
- x
2
+ 4xy - 4y
2
S o l u t i o n :
9z2-x2+4xy-4y2=9z2-(x2-4xy+4y2)=9z2-[x2-2×x×2y+(2y)2]=(3z)2-(x-2y)2=[3z-(x-2y)][3z+(x-2y)]=(3z-x+2y)(3z+x-2y)=(x-2y+3z)(-x+2y+3z)
Q u e s t i o n : 1 2 6
Factorize each of the following algebraic expression:
9a
4
- 24a
2
b
2
+ 16b
4
- 256
S o l u t i o n :
9a4-24a2b2+16b4-256=(9a4-24a2b2+16b4)-256=[(3a2)2-2×3a2×4b2+(4b2)2]-162=(3a2-4b2)2-162=[(3a2-4b2)-16][(3a2-4b2)+16]=(3a2-4b2-16)(3a2-4b2+16)
Q u e s t i o n : 1 2 7
Factorize each of the following algebraic expression:
16 - a
6
+ 4a
3
b
3
- 4b
6
S o l u t i o n :
16-a6+4a3b3-4b6=16-(a6-4a3b3+4b6)=42-[(a3)2-2×a3×2b3+(2b3)2]=42-(a3-2b3)2=[4-(a3-2b3)][4+(a3-2b3)]=(4-a3+2b3)(4+a3-2b3)=(a3-2b3+4)(-a3+2b3+4)
Q u e s t i o n : 1 2 8
Factorize each of the following algebraic expression:
a
2
- 2ab + b
2
- c
2
S o l u t i o n :
a2-2ab+b2-c2=(a2-2ab+b2)-c2=(a2-2×a×b+b2)-c2=(a-b)2-c2=[(a-b)-c][(a-b)+c]=(a-b-c)(a-b+c)
Q u e s t i o n : 1 2 9
Factorize each of the following algebraic expression:
x
2
+ 2x + 1 - 9y
2
S o l u t i o n :
x2+2x+1-9y2=(x2+2x+1)-9y2=(x2+2×x×1+1)-9y2=(x+1)2-(3y)2=[(x+1)-3y][(x+1)+3y]=(x+1-3y)(x+1+3y)=(x+3y+1)(x-3y+1)
Q u e s t i o n : 1 3 0
Factorize each of the following algebraic expression:
a
2
+ 4ab + 3b
2
S o l u t i o n :
a2+4ab+3b2=a2+4ab+4b2-b2=[a2+2×a×2b+(2b)2]-b2=(a+2b)2-b2=[(a+2b)-b][(a+2b)+b]=(a+2b-b)(a+2b+b)=(a+b)(a+3b)
Q u e s t i o n : 1 3 1
Factorize each of the following algebraic expression:
96 - 4x - x
2
S o l u t i o n :
96-4x-x2=100-4-4x-x2=100-(x2+4x+4)=100-(x2+2×x×2+22)=102-(x+2)2=[10-(x+2)][10+(x+2)]=(10-x-2)(10+x+2)=(8-x)(12+x)=(x+12)(-x+8)
Q u e s t i o n : 1 3 2
Factorize each of the following algebraic expression:
a
4
+ 3a
2
+4
S o l u t i o n :
a4+3a2+4=a4+4a2-a2+4=(a4+4a2+4)-a2=[(a2)2+2×a2×2+22]-a2=(a2+2)2-a2=[(a2+2)-a][(a2+2)+a]=(a2-a+2)((a2+a+2)
Q u e s t i o n : 1 3 3
Factorize each of the following algebraic expression:
4x
4
+ 1
S o l u t i o n :
4x4+1=4x4+4x2+1-4x2=[(2x2)2+2×2x2×1+1]-4x2=(2x2+1)2-(2x)2=[(2x2+1)-2x][(2x2+1)+2x]=(2x2-2x+1)(2x2+2x+1)
Q u e s t i o n : 1 3 4
Factorize each of the following algebraic expression:
4x
4
+ y
4
S o l u t i o n :
4x4+y4=4x4+4x2y2+y4-4x2y2=[(2x2)2+2×2x2×y+(y2)2]-(2xy)2=(2x2+y2)2-(2xy)2=[(2x2+y2)-2xy][(2x2+y2)+2xy]=(2x2-2xy+y2)(2x2+2xy+y2)
Q u e s t i o n : 1 3 5
Factorize each of the following algebraic expression:
(x + 2)
2
- 6(x + 2) + 9
S o l u t i o n :
(x+2)2-6(x+2)+9=(x+2)2-2×(x+2)×3+32=[(x+2)-3]2=(x+2-3)2=(x-1)2=(x-1)(x-1)
Q u e s t i o n : 1 3 6
Factorize each of the following algebraic expression:
25 - p
2
- q
2
- 2pq
S o l u t i o n :
25-p2-q2-2pq=25-(p2+2pq+q2)=52-(p2+2×p×q+q2)=52-(p+q)2=[5-(p+q)][5+(p+q)]=(5-p-q)(5+p+q)=-(p+q-5)(p+q+5)
Q u e s t i o n : 1 3 7
Factorize each of the following algebraic expression:
x
2
+ 9y
2
- 6xy - 25a
2
S o l u t i o n :
x2+9y2-6xy-25a2=(x2-6xy+9y2)-25a2=[x2-2×x×3y+(3y)2]-25a2=(x-3y)2-(5a)2=[(x-3y)-5a][(x-3y)+5a]=(x-3y-5a)(x-3y+5a)
Q u e s t i o n : 1 3 8
Factorize each of the following algebraic expression:
49 - a
2
+ 8ab - 16b
2
S o l u t i o n :
49-a2+8ab-16b2=49-(a2-8ab+16b2)=49-[a2-2×a×4b+(4b)2]=72-(a-4b)2=[7-(a-4b)][7+(a-4b)]=(7-a+4b)(7+a-4b)=-(a-4b-7)(a-4b+7)=-(a-4b+7)(a-4b-7)
Q u e s t i o n : 1 3 9
Factorize each of the following algebraic expression:
a
2
- 8ab + 16b
2
- 25c
2
S o l u t i o n :
a2-8ab+16b2-25c2=(a2-8ab+16b2)-25c2=[a2-2×a×4b+(4b)2]-25c2=(a-4b)2-(5c)2=[(a-4b)-5c][(a-4b)+5c]=(a-4b-5c)(a-4b+5c)
Q u e s t i o n : 1 4 0
Factorize each of the following algebraic expression:
x
2
- y
2
+ 6y - 9
S o l u t i o n :
x2-y2+6y-9=x2-(y2-6y+9)=x2-(y2-2×y×3+32)=x2-(y-3)2=[x-(y-3)][x+(y-3)]=(x-y+3)(x+y-3)
Q u e s t i o n : 1 4 1
Factorize each of the following algebraic expression:
25x
2
- 10x + 1 - 36y
2
S o l u t i o n :
25x2-10x+1-36y2=(25x2-10x+1)-36y2=[(5x)2-2×5x×1+1]-36y2=(5x-1)2-(6y)2=[(5x-1)-6y][(5x-1)+6y]=(5x-1-6y)(5x-1+6y)=(5x-6y-1)(5x+6y-1)
Q u e s t i o n : 1 4 2
Factorize each of the following algebraic expression:
a
2
- b
2
+ 2bc - c
2
S o l u t i o n :
a2-b2+2bc-c2=a2-(b2-2bc+c2)=a2-(b2-2×b×c+c2)=a2-(b-c)2=[(a-(b-c)][(a+(b-c)]=(a-b+c)(a+b-c)
Page 3
Q u e s t i o n : 1 2 0
Factorize each of the following algebraic expression:
4x
2
+ 12xy +9y
2
S o l u t i o n :
4x2+12xy+9y2=(2x)2+2×2x×3y+(3y)2=(2x+3y)2=(2x+3y)(2x+3y)
Q u e s t i o n : 1 2 1
Factorize each of the following algebraic expression:
9a
2
- 24ab + 16b
2
S o l u t i o n :
9a2-24ab+16b2=(3a)2-2×3a×4b+(4b)2=(3a-4b)2=(3a-4b)(3a-4b)
Q u e s t i o n : 1 2 2
Factorize each of the following algebraic expression:
p
2
q
2
- 6pqr + 9r
2
S o l u t i o n :
p2q2-6pqr+9r2=(pq)2-2×pq×3r+(3r)2=(pq-3r)2=(pq-3r)(pq-3r)
Q u e s t i o n : 1 2 3
Factorize each of the following algebraic expression:
36a
2
+ 36a + 9
S o l u t i o n :
36a2+36a+9=9(4a2+4a+1)=9(2a)2+2×2a×1+12=9(2a+1)2=9(2a+1)(2a+1)
Q u e s t i o n : 1 2 4
Factorize each of the following algebraic expression:
a
2
+ 2ab + b
2
- 16
S o l u t i o n :
a2+2ab+b2-16=a2+2×a×b+b2-16=(a+b)2-42=(a+b-4)(a+b+4)
Q u e s t i o n : 1 2 5
Factorize each of the following algebraic expression:
9z
2
- x
2
+ 4xy - 4y
2
S o l u t i o n :
9z2-x2+4xy-4y2=9z2-(x2-4xy+4y2)=9z2-[x2-2×x×2y+(2y)2]=(3z)2-(x-2y)2=[3z-(x-2y)][3z+(x-2y)]=(3z-x+2y)(3z+x-2y)=(x-2y+3z)(-x+2y+3z)
Q u e s t i o n : 1 2 6
Factorize each of the following algebraic expression:
9a
4
- 24a
2
b
2
+ 16b
4
- 256
S o l u t i o n :
9a4-24a2b2+16b4-256=(9a4-24a2b2+16b4)-256=[(3a2)2-2×3a2×4b2+(4b2)2]-162=(3a2-4b2)2-162=[(3a2-4b2)-16][(3a2-4b2)+16]=(3a2-4b2-16)(3a2-4b2+16)
Q u e s t i o n : 1 2 7
Factorize each of the following algebraic expression:
16 - a
6
+ 4a
3
b
3
- 4b
6
S o l u t i o n :
16-a6+4a3b3-4b6=16-(a6-4a3b3+4b6)=42-[(a3)2-2×a3×2b3+(2b3)2]=42-(a3-2b3)2=[4-(a3-2b3)][4+(a3-2b3)]=(4-a3+2b3)(4+a3-2b3)=(a3-2b3+4)(-a3+2b3+4)
Q u e s t i o n : 1 2 8
Factorize each of the following algebraic expression:
a
2
- 2ab + b
2
- c
2
S o l u t i o n :
a2-2ab+b2-c2=(a2-2ab+b2)-c2=(a2-2×a×b+b2)-c2=(a-b)2-c2=[(a-b)-c][(a-b)+c]=(a-b-c)(a-b+c)
Q u e s t i o n : 1 2 9
Factorize each of the following algebraic expression:
x
2
+ 2x + 1 - 9y
2
S o l u t i o n :
x2+2x+1-9y2=(x2+2x+1)-9y2=(x2+2×x×1+1)-9y2=(x+1)2-(3y)2=[(x+1)-3y][(x+1)+3y]=(x+1-3y)(x+1+3y)=(x+3y+1)(x-3y+1)
Q u e s t i o n : 1 3 0
Factorize each of the following algebraic expression:
a
2
+ 4ab + 3b
2
S o l u t i o n :
a2+4ab+3b2=a2+4ab+4b2-b2=[a2+2×a×2b+(2b)2]-b2=(a+2b)2-b2=[(a+2b)-b][(a+2b)+b]=(a+2b-b)(a+2b+b)=(a+b)(a+3b)
Q u e s t i o n : 1 3 1
Factorize each of the following algebraic expression:
96 - 4x - x
2
S o l u t i o n :
96-4x-x2=100-4-4x-x2=100-(x2+4x+4)=100-(x2+2×x×2+22)=102-(x+2)2=[10-(x+2)][10+(x+2)]=(10-x-2)(10+x+2)=(8-x)(12+x)=(x+12)(-x+8)
Q u e s t i o n : 1 3 2
Factorize each of the following algebraic expression:
a
4
+ 3a
2
+4
S o l u t i o n :
a4+3a2+4=a4+4a2-a2+4=(a4+4a2+4)-a2=[(a2)2+2×a2×2+22]-a2=(a2+2)2-a2=[(a2+2)-a][(a2+2)+a]=(a2-a+2)((a2+a+2)
Q u e s t i o n : 1 3 3
Factorize each of the following algebraic expression:
4x
4
+ 1
S o l u t i o n :
4x4+1=4x4+4x2+1-4x2=[(2x2)2+2×2x2×1+1]-4x2=(2x2+1)2-(2x)2=[(2x2+1)-2x][(2x2+1)+2x]=(2x2-2x+1)(2x2+2x+1)
Q u e s t i o n : 1 3 4
Factorize each of the following algebraic expression:
4x
4
+ y
4
S o l u t i o n :
4x4+y4=4x4+4x2y2+y4-4x2y2=[(2x2)2+2×2x2×y+(y2)2]-(2xy)2=(2x2+y2)2-(2xy)2=[(2x2+y2)-2xy][(2x2+y2)+2xy]=(2x2-2xy+y2)(2x2+2xy+y2)
Q u e s t i o n : 1 3 5
Factorize each of the following algebraic expression:
(x + 2)
2
- 6(x + 2) + 9
S o l u t i o n :
(x+2)2-6(x+2)+9=(x+2)2-2×(x+2)×3+32=[(x+2)-3]2=(x+2-3)2=(x-1)2=(x-1)(x-1)
Q u e s t i o n : 1 3 6
Factorize each of the following algebraic expression:
25 - p
2
- q
2
- 2pq
S o l u t i o n :
25-p2-q2-2pq=25-(p2+2pq+q2)=52-(p2+2×p×q+q2)=52-(p+q)2=[5-(p+q)][5+(p+q)]=(5-p-q)(5+p+q)=-(p+q-5)(p+q+5)
Q u e s t i o n : 1 3 7
Factorize each of the following algebraic expression:
x
2
+ 9y
2
- 6xy - 25a
2
S o l u t i o n :
x2+9y2-6xy-25a2=(x2-6xy+9y2)-25a2=[x2-2×x×3y+(3y)2]-25a2=(x-3y)2-(5a)2=[(x-3y)-5a][(x-3y)+5a]=(x-3y-5a)(x-3y+5a)
Q u e s t i o n : 1 3 8
Factorize each of the following algebraic expression:
49 - a
2
+ 8ab - 16b
2
S o l u t i o n :
49-a2+8ab-16b2=49-(a2-8ab+16b2)=49-[a2-2×a×4b+(4b)2]=72-(a-4b)2=[7-(a-4b)][7+(a-4b)]=(7-a+4b)(7+a-4b)=-(a-4b-7)(a-4b+7)=-(a-4b+7)(a-4b-7)
Q u e s t i o n : 1 3 9
Factorize each of the following algebraic expression:
a
2
- 8ab + 16b
2
- 25c
2
S o l u t i o n :
a2-8ab+16b2-25c2=(a2-8ab+16b2)-25c2=[a2-2×a×4b+(4b)2]-25c2=(a-4b)2-(5c)2=[(a-4b)-5c][(a-4b)+5c]=(a-4b-5c)(a-4b+5c)
Q u e s t i o n : 1 4 0
Factorize each of the following algebraic expression:
x
2
- y
2
+ 6y - 9
S o l u t i o n :
x2-y2+6y-9=x2-(y2-6y+9)=x2-(y2-2×y×3+32)=x2-(y-3)2=[x-(y-3)][x+(y-3)]=(x-y+3)(x+y-3)
Q u e s t i o n : 1 4 1
Factorize each of the following algebraic expression:
25x
2
- 10x + 1 - 36y
2
S o l u t i o n :
25x2-10x+1-36y2=(25x2-10x+1)-36y2=[(5x)2-2×5x×1+1]-36y2=(5x-1)2-(6y)2=[(5x-1)-6y][(5x-1)+6y]=(5x-1-6y)(5x-1+6y)=(5x-6y-1)(5x+6y-1)
Q u e s t i o n : 1 4 2
Factorize each of the following algebraic expression:
a
2
- b
2
+ 2bc - c
2
S o l u t i o n :
a2-b2+2bc-c2=a2-(b2-2bc+c2)=a2-(b2-2×b×c+c2)=a2-(b-c)2=[(a-(b-c)][(a+(b-c)]=(a-b+c)(a+b-c)
Q u e s t i o n : 1 4 3
Factorize each of the following algebraic expression:
a
2
+ 2ab + b
2
- c
2
S o l u t i o n :
a2+2ab+b2-c2=(a2+2ab+b2)-c2=(a2+2×a×b+b2)-c2=(a+b)2-c2=[(a+b)-c][(a+b)+c]=(a+b-c)(a+b+c)
Q u e s t i o n : 1 4 4
Factorize each of the following algebraic expression:
49 - x
2
- y
2
+ 2xy
S o l u t i o n :
49-x2-y2+2xy=49-(x2-2xy+y2)=49-(x2-2×x×y+y2)=72-(x-y)2=[7-(x-y)][7+(x-y)]=(7-x+y)(7+x-y)=(x-y+7)(y-x+7)
Q u e s t i o n : 1 4 5
Factorize each of the following algebraic expression:
a
2
+ 4b
2
- 4ab - 4c
2
S o l u t i o n :
a2+4b2-4ab-4c2=(a2-4ab+4b2)-4c2=[a2-2×a×2b+(2b)2]-4c2=(a-2b)2-(2c)2=[(a-2b)-2c][(a-2b)+2c]=(a-2b-2c)(a-2b+2c)
Q u e s t i o n : 1 4 6
Factorize each of the following algebraic expression:
x
2
- y
2
- 4xz + 4z
2
S o l u t i o n :
x2-y2-4xz+4z2=(x2-4xz+4z2)-y2=[x2-2×x×2z+(2z)2]-y2=(x-2z)2-y2=[(x-2z)-y][(x-2z)+y]=(x-2z-y)(x-2z+y)=(x+y-2z)(x-y-2z)
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Document Description: Factorization - Exercise 7.6 for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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