S.chand publication New Learning Composite mathematics solution of class 8 Chapter 6 Factorisation of Algebraic Expressions Exercise 6G

 Exercise 6G

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Q1 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Factorise:

Question 1

2x² + 11x + 15

Sol :

=2x²+6x+5x+15

=2x(x+3)+5(x+3)

=(2x+5)(x+3)

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Q2 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 2

6x² + 17x + 5

Sol :

=6x²+15x+2x+5

=3x(2x+5)+1(2x+5)

=(3x+1)(2x+5)

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Q3 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 3

3x² + 11x + 10

Sol :
=3x²+6x+5x+10

=3x(x+2)+5(x+2)

=(3x+5)(x+2)

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Question 4

5b² + 16b + 3

Sol :
=5b²+15b+b+3

=5b(b+3)+1(b+3)

=(b+3)(5b+1)

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Question 5

3x² + 13x + 12

Sol :

=3x²+9x+4x+12

=3x(x+3)+4(x+3)

=(x+3)(3x+4)

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Q6 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 6

2x² + 17x + 21

Sol :

=2x²+14x+3x+21

=2x(x+7)+3(x+7)

=(2x+3)(x+7)

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Q7 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 7

15y² + 16y + 4

Sol :

=15y²+10y+6y+4

=5y(3y+2)+2(3y+2)

=(3y+2)(5y+2)

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Q8 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 8

6x² – 17x -14

Sol :

=6x²–21x-4x-14

=3x(2x+7)-2(2x+7)

=(2x+7)(3x-2)

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Question 9

4m² + 7m – 2

Sol :

=4m²+8m-m-2

=4m(m+2)-1(m+2)

=(m+2)(4m-1)

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Question 10

2x² – 7x – 15

Sol :

=2x²–10x+3x-15

=2x(x-5)+3(x-5)

=(x-5)(2x+3)

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Question 11

5x² – 16x + 3

Sol :

=5x²–15x-x+3

=5x(x-3)-1(x-3)

=(x-3)(5x-1)

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Q12 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 12

6x² – 17x + 12

Sol :

=6x²-9x-8x+12

=3x(2x-3)-4(2x-3)

=(2x-3)(3x-4)

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Question 13

5x² + 9x – 18

Sol :

=5x²+15x-6x-18

=5x(x+3)-6(x+3)

=(x+3)(5x-6)

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Q14 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 14

3x² – x – 4

Sol :
=3x²–4x+3x-4

=x(3x-4)+1(3x-4)

=(3x-4)(x+1)

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Q15 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 15

8a² + 18a – 5

Sol :

=8a²+20a-2a-5

=4a(2a+5)-1(2a+5)

=(2a+5)(4a-1)

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Question 16

8x² – 73x + 9

Sol :

=8x²–72x-x+9

=8x(x-9)-1(x-9)

=(x-9)(8x-1)

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Q17 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 17

-2x² + 5x + 42

Sol :

=-2x²+12x-7x+42

=-2x(x-6)-7(x-6)

=(x-6)(-2x-7)

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Q18 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 18

-12x² – 35x – 18

Sol :
=-12x²–27x-8x-18

=-3x(4x+9)-2(4x+9)

=(4x+9)(-3x-2)

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Q19 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 19

-2x² – 15x – 7

Sol :
=-2x²–14x-x-7

=-2x(x+7)-1(x+7)

=(x+7)(-2x-1)

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Q20 | Ex-6G | Class 8 | SChand |New Learning Composite maths | Factorisation of Algebraic Expressions| myhelper

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Question 20

30t² + 39t – 9

Sol :

=30t²+45t-6t-9

=15t(2t+3)-3(2t+3)

=(2t+3)(15t-3)

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Question 21

15x⁴ – 10x³ – 25x²

Sol :

=5x²(3x²-5x+3x-5)

=5x²[x(3x-5)+1(3x-5)]

=5x²[(3x-5)(x+1)]

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Question 22

14x³ – 57x²y – 27xy²

Sol :

=14x³–63x²y+6x²y-27xy²

=7x²(2x-9y)+3xy(2x-9y)

=(2x-9y)(7x²+3xy)

=x(7x+3y)(2x-9y)

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Question 23

-3x³ + 16x² – 16x

Sol :

=x(-3x²+16x–16)

=x[-3x²+16x-16]

=x[-3x²+12x+4x-16]

=x[-3x(x-4)+4(x-4)]

=x[(x-4)(-3x+4)]

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Question 24

-4x⁴ – 4x³ + 15x²

Sol :

=x²(-4x²-4x+15)

=x²(-4x²-10x+6x+15)

=x²[-2x(2x-5)+3(x-5)]

=x²[(2x-5)(-2x+3)]

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Question 25

56x³ + 15x² – 56x

Sol :

=x(56x²+15x-56)

=x[56x²-49x+64x-56]

=x[7x(8x-7)+8(8x-7)]

=x(8x-7)(7x+8)

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Question 26

32x⁴ + 12x³y – 5x²y²

Sol :
=32x⁴+20x³y-8x³y-5x²y²

=4x³(8x+5y)-x²y(8x+5y)

=(8x+5y)(4x³-x²y)

=x²(4x-y)(8x+5y)

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Question 27

30m² – 78mn + 36n²

Sol :

=30m²–60mn-18mn+36n²

=30m(m-n)-18n(m-n)

=(m-2n)(30m-18n)

=6(5m-3n)(m-2n)