Factorisation Class 9 RS Aggarwal Exe-4A Goyal Brothers ICSE Maths Solutions Ch-4. In this article you will learn Factorisation by taking out common and grouping method easily. Visit official Website CISCE for detail information about ICSE Board Class-9
Factorisation Class 9 RS Aggarwal Exe-4A Goyal Brothers ICSE Maths Solutions Ch-4
| Board | ICSE |
| Subject | Maths |
| Class | 9th |
| Chapter-4 | Factorisation |
| Writer | RS Aggrawal |
| Topics | Factorisation by taking out common and grouping |
| Academic Session | 2024-2025 |
Factorisation by Taking Out Common and Grouping
Common Method: take out the highest common factor and place it in front of the brackets. Then the expression inside the brackets is obtained by dividing each term by the highest common factor.
Grouping Method: Group terms with common factors. Factor out the common factor in each group. Factor the common factor from the expression. Check by multiplying the factors
Exercise- 4A
Factorisation Class 9 RS Aggarwal Exe-4A Goyal Brothers ICSE Maths Solutions Ch-4
Page- 58,59
Factorise :
Que-1: 5x²-20xy
Sol: 5x²-20xy
5x(x-4y).
Que-2: 18a²b-24abc
Sol: 18a²b-24abc
6ab(3a-4c).
Que-3: 27x³y³-45x^4y²
Sol: 27x³y³-45x^4y²
9x³y²(3y-5x).
Que-4: 5a(b+c) – 7b(b+c)
Sol: 5a(b+c) – 7b(b+c)
(b+c)(5a-7b).
Que-5: 2x(p²+q²) + 4y(p²+q²)
Sol: 2x(p²+q²) + 4y(p²+q²)
(p²+q²)(2x+4y)
2(p²+q²)(2x+4y).
Que-6: x(a-5)+y(5-a)
Sol: x(a-5)+y(5-a)
x(a-5)-y(a-5)
(x-y)(a-5).
Que-7: 4(x+y)-6(x+y)²
Sol: 4(x+y)-6(x+y)²
2(x+y)(2-3x-3y).
Que-8: 6(2a+3b)² – 8(2a+3b)
Sol: 6(2a+3b)² – 8(2a+3b)
2(2a+3b)(6a+9b-4)
Que-9: x(x+y)³ – 3x²y(x+y)
Sol: x(x+y)³ – 3x²y(x+y)
x(x+y)(x²+y²)-3xy
x(x+y)(x²+y²+2xy-3xy)
x(x+y)(x²+y²-xy)
Que-10: a³+2a²+5a+10
Sol: a³+2a²+5a+10
a²(a+2)+5(a+2)(a+2)(a²+5).
Que-11: x²+xy-2xz-2yz
Sol: x²+xy-2xz-2yz
x(x+y) -2z(x+y)
(x+y)(x-2z).
Que-12: a³b-a²b+5ab-5b
Sol: a³b-a²b+5ab-5b
a²b(a-1)+5b(a-1)
(a-1)(a²b+5b)
b(a²+5)(a-1).
Que-13: x²+y-xy-x
Sol: x²+y-xy-x
x²-x-xy+y
x(x-1)-y(x-1)
(x-y)(x-1).
Que-14: a(a+b-c)-bc
Sol: a(a+b-c)-bc
a²+ab-ac-bc
a(a+b)-c(a+b)
(a+b)(a-c).
Que-15: (4a-1)² – 8a+2
Sol: (4a-1)² – 8a+2
16a²+1-8a-8a+2
16a²-16a+3
16a²-4a-12a+3
4a(4a-1)-3(4a-1)
(4a-1)(4a-3).
Que-16: 8-4a-2a³+a^4
Sol: 8-4a-2a³+a^4
4(2-a)-a³(2-a)
(4-a³)(2-a).
Que-17: 2a²+bc-2ab-ac
Sol: 2a²+bc-2ab-ac
2a²-2ab+bc-ac
2a(a-b)+c(a-b)
(a-b)(2a+c).
Que-18: a(a-2b-c)+2bc
Sol: a(a-2b-c)+2bc
a²-2ab-ac+2bc
a(a-2b)-c(a-2b)
(a-c)(a-2b).
Que-19: x²-(a+b)x+ab
Sol: x²-(a+b)x+ab
x²-ax+bx+ab
x(x-a)-b(x-a)
(x-a)(x-b).
Que-20: 3ax-6ay-8by+4bx
Sol: 3ax-6ay-8by+4bx
3ax-6ay+4bx-8by
3a(x-2y)+4b(x-2y)
(3a+4b)(x-2y).
Que-21: ab(x²+y²)-xy(a²+b²)
Sol: ab(x²+y²)-xy(a²+b²)
abx²+aby²-a²xy-b²xy
abx²-a²xy-b²xy+aby²
ax(bx-ay)-by(bx-ay)
(ax-by)(bx-ay).
Que-22: ab(x²+1)+x(a²+b²)
Sol: ab(a²+1)+x(a²+b²)
abx²+ab+xa²+xb²
abx²+xa²+xb²+ab
ax(bx+a)+b(bx+a)
(ax+b)(bx+a).
Que-23: a³+ab(1-2a)-2b²
Sol: a³+ab(1-2a)-2b²
a³+ab-2a²b-2b²
a(a²+b)-2b(a²+b)
(a-2b)(a²+b).
Que-24: x²+(1/x²)-2-3x+(3/x)
Sol: x²+(1/x²)-2-3x+(3/x)
[x-(1/x)]² – 3[x-(1/x)]
[x-(1/x)][x-(1/x)-3].
– : End of Factorisation Class 9 RS Aggarwal Exe-4A Goyal Brothers ICSE Maths Solutions :–
Return to : – RS Aggarwal Solutions for ICSE Class-9 Mathematics
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