Factorization - Exercise 7.3 | Mathematics (Maths) Class 8 PDF Download

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Q u e s t i o n : 3 5
Factorize each of the following algebraic expressions:
6x(2x - y) + 7y(2x - y)
S o l u t i o n :
6x(2x -y)+7y(2x -y) = (6x +7y)(2x -y)         [Taking (2x -y) as the common factor]
Q u e s t i o n : 3 6
Factorize each of the following algebraic expressions:
2r(y - x) + s(x - y)
S o l u t i o n :
2r(y -x)+s(x -y) = 2r(y -x)-s(y -x)      [ ? (x -y) = -(y -x)] = (2r-s)(y -x)              [Taking (y -x) as the common factor]
Q u e s t i o n : 3 7
Factorize each of the following algebraic expressions:
7a(2x - 3) + 3b(2x - 3)
S o l u t i o n :
7a(2x -3)+3b(2x -3) = (7a +3b)(2x -3)            [Taking (2x -3) as the common factor]
Q u e s t i o n : 3 8
Factorize each of the following algebraic expressions:
9a(6a - 5b) -12a
2
(6a - 5b)
S o l u t i o n :
9a 6a -5b -12a
2
6a -5b = 9a -12a
2
6a -5b     Taking 6a -5b as the common factor = 3a 3 -4a 6a -5b       Taking 3a as the common factor of the quadratic 9a -12a
2
Q u e s t i o n : 3 9
Factorize each of the following algebraic expressions:
5(x - 2y)
2
 + 3(x - 2y)
S o l u t i o n :
5 x -2y)
2
+3 x -2y = 5 x -2y +3 x -2y     Taking x -2y as the common factor = 5x -10y +3 x -2y
Q u e s t i o n : 4 0
Factorize each of the following algebraic expressions:
16(2l - 3m)
2
 -12(3m - 2l)
S o l u t i o n :
16 2l -3m)
2
-12 3m -2l = 16 2l -3m)
2
+12 2l -3m            ? 3m -2l = - 2l -3m = 16 2l -3m +12 2l -3m           Taking 2l -3m as the common factor = 4 4 2l -3m +3 2l -3m
Q u e s t i o n : 4 1
Factorize each of the following algebraic expressions:
3a(x - 2y) -b(x - 2y)
S o l u t i o n :
3a(x -2y)-b(x -2y) = (3a -b)(x -2y)           [Taking (x -2y) as the common factor]
Q u e s t i o n : 4 2
Factorize each of the following algebraic expressions:
a
2
(x + y) +b
2
(x + y) +c
2
(x + y)
S o l u t i o n :
a
2
x +y +b
2
x +y +c
2
x +y = a
2
+b
2
+c
2
x +y                      Taking x +y as the common factor
Q u e s t i o n : 4 3
Factorize each of the following algebraic expressions:
(x - y)
2
 + (x - y)
S o l u t i o n :
x -y)
2
+ x -y = x -y x -y + x -y   Taking x -y as the common factor = x -y +1 x -y
Q u e s t i o n : 4 4
Factorize each of the following algebraic expressions:
6(a + 2b) -4(a + 2b)
2
S o l u t i o n :
6 a +2b -4 a +2b)
2
= 6 -4 a +2b a +2b      Taking a +2b as the common factor = 2 3 -2 a +2b a +2b   Taking 2 as the common factor of 6 -4 a +2b = 2 3 -2a -4b a +2
Q u e s t i o n : 4 5
Factorize each of the following algebraic expressions:
a(x - y) + 2b(y - x) + c(x - y)
2
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Q u e s t i o n : 3 5
Factorize each of the following algebraic expressions:
6x(2x - y) + 7y(2x - y)
S o l u t i o n :
6x(2x -y)+7y(2x -y) = (6x +7y)(2x -y)         [Taking (2x -y) as the common factor]
Q u e s t i o n : 3 6
Factorize each of the following algebraic expressions:
2r(y - x) + s(x - y)
S o l u t i o n :
2r(y -x)+s(x -y) = 2r(y -x)-s(y -x)      [ ? (x -y) = -(y -x)] = (2r-s)(y -x)              [Taking (y -x) as the common factor]
Q u e s t i o n : 3 7
Factorize each of the following algebraic expressions:
7a(2x - 3) + 3b(2x - 3)
S o l u t i o n :
7a(2x -3)+3b(2x -3) = (7a +3b)(2x -3)            [Taking (2x -3) as the common factor]
Q u e s t i o n : 3 8
Factorize each of the following algebraic expressions:
9a(6a - 5b) -12a
2
(6a - 5b)
S o l u t i o n :
9a 6a -5b -12a
2
6a -5b = 9a -12a
2
6a -5b     Taking 6a -5b as the common factor = 3a 3 -4a 6a -5b       Taking 3a as the common factor of the quadratic 9a -12a
2
Q u e s t i o n : 3 9
Factorize each of the following algebraic expressions:
5(x - 2y)
2
 + 3(x - 2y)
S o l u t i o n :
5 x -2y)
2
+3 x -2y = 5 x -2y +3 x -2y     Taking x -2y as the common factor = 5x -10y +3 x -2y
Q u e s t i o n : 4 0
Factorize each of the following algebraic expressions:
16(2l - 3m)
2
 -12(3m - 2l)
S o l u t i o n :
16 2l -3m)
2
-12 3m -2l = 16 2l -3m)
2
+12 2l -3m            ? 3m -2l = - 2l -3m = 16 2l -3m +12 2l -3m           Taking 2l -3m as the common factor = 4 4 2l -3m +3 2l -3m
Q u e s t i o n : 4 1
Factorize each of the following algebraic expressions:
3a(x - 2y) -b(x - 2y)
S o l u t i o n :
3a(x -2y)-b(x -2y) = (3a -b)(x -2y)           [Taking (x -2y) as the common factor]
Q u e s t i o n : 4 2
Factorize each of the following algebraic expressions:
a
2
(x + y) +b
2
(x + y) +c
2
(x + y)
S o l u t i o n :
a
2
x +y +b
2
x +y +c
2
x +y = a
2
+b
2
+c
2
x +y                      Taking x +y as the common factor
Q u e s t i o n : 4 3
Factorize each of the following algebraic expressions:
(x - y)
2
 + (x - y)
S o l u t i o n :
x -y)
2
+ x -y = x -y x -y + x -y   Taking x -y as the common factor = x -y +1 x -y
Q u e s t i o n : 4 4
Factorize each of the following algebraic expressions:
6(a + 2b) -4(a + 2b)
2
S o l u t i o n :
6 a +2b -4 a +2b)
2
= 6 -4 a +2b a +2b      Taking a +2b as the common factor = 2 3 -2 a +2b a +2b   Taking 2 as the common factor of 6 -4 a +2b = 2 3 -2a -4b a +2
Q u e s t i o n : 4 5
Factorize each of the following algebraic expressions:
a(x - y) + 2b(y - x) + c(x - y)
2
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( ( ) [ ( ) ]( ) [ ( ) ] ( ) ( )
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S o l u t i o n :
a x -y +2b y -x +c x -y)
2
= a x -y -2b x -y +c x -y)
2
   ? y -x = - x -y = a -2b +c x -y x -y = a -2b +cx -cy x -y
Q u e s t i o n : 4 6
Factorize each of the following algebraic expressions:
-4(x - 2y)
2
 + 8(x -2y)
S o l u t i o n :
-4 x -2y)
2
+8 x -2y = -4 x -2y +8 x -2y   Taking x -2y as the common factor = 4 - x -2y +2 x -2y   Taking 4 as the common factor of -4 x -2y +8 = 4 2y -x +2 x -2y
Q u e s t i o n : 4 7
Factorize each of the following algebraic expressions:
x
3
(a - 2b) + x
2
(a - 2b)
S o l u t i o n :
x
3
a -2b +x
2
a -2b = x
3
+x
2
a -2b       Taking a -2b as the common factor = x
2
x +1 a -2b      Taking x
2
 as the common factor of x
3
+x
2
Q u e s t i o n : 4 8
Factorize each of the following algebraic expressions:
(2x - 3y)(a + b) + (3x - 2y)(a + b)
S o l u t i o n :
(2x -3y)(a +b)+(3x -2y)(a +b) = (2x -3y +3x -2y)(a +b)   [Taking (a +b) as the common factor] = (5x -5y)(a +b) = 5(x -y)(a +b)                      [Taking 5 as the common factor of (5x -5y)]
Q u e s t i o n : 4 9
Factorize each of the following algebraic expressions:
4(x + y) (3a - b) +6(x + y) (2b - 3a)
S o l u t i o n :
4(x +y)(3a -b)+6(x +y)(2b -3a) = 2(x +y)[2(3a -b)+3(2b -3a)]                {Taking [2 (x +y)] as the common factor} = 2(x +y)(6a -2b +6b -9a) = 2(x +y)(4b -3a)
     
      
                        
     
      
                             
     
      
                     
     
      
                          
     
      
                             
     
      
                         
     
      
                           
     
      
                                                              
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