ML Aggarwal Solution Class 9 Chapter 4 Factorisation Exercise 4.4

 Exercise 4.4

Question 1

(i) x2+5x+6

⇒x2+3x+2x+6

⇒x(x+3)+2(x+3)

⇒(x+3)(x+2)


(ii) x2-8x+7

⇒x2-7x-x+7

⇒x(x-7)-1(x-7)

⇒(x-7)(x-1)


Question 2

(i) x2+6x-7

⇒x2+7x-x-7

⇒x(x+7)-1(x+7)

⇒(x+7)(x-1)


(ii) y2+7y-18

⇒y2+9y-2y-18

⇒y(y+9)-2(y+9)

⇒(y+9)(y-2)


(iii) a2-3a-54

⇒a2-9a+a-54

⇒a(a-9)+6(a-9)

⇒(a-9)(a+6)


Question 4

(i) 2x2-7x+6

⇒2x2-4x-3x+6

⇒2x(x-2)-3(x-2)

⇒(x-2)(2x-3)


(ii) 6x2+13x-5

⇒6x2+15x-2x-5

⇒3x(2x+5)-1(2x+5)

⇒(2x+5)(3x-1)


Question 5

(i) 6x2+11x-10

⇒6x2+15x-4x-10

⇒3x(2x+5)-2(2x+5)

⇒(2x+5)(3x-2)


(ii) 6x2-7x-3

⇒6x2-9x+2x-3

⇒3x(2x-3)+1(2x-3)

⇒(2x-3)(3x+1)


Question 6

(i) 2x2-x-6

⇒2x2-4x+3x-6

⇒2x(x-2)+3(x-2)

⇒(x-2)(2x+3)


(ii) 1-18y-63y2

⇒1-21y+3y-63y2

⇒1(1-21y)+3y(1-21y)

⇒(1-21y)(1+3y)


Question 7

(i) 2y2+y-45

⇒2y2+10y-9y-45

⇒2y(y+5)-9(y+5)

⇒(y+5)(2y-9)


(ii) 5-4x-12x2

⇒5-10x+6x-12x2

⇒5(1-2x)+6x(1-2x)

⇒(1-2x)(5+6x)


Question 8

(i) x(12x+7)-10

⇒12x2+7x-10

⇒12x2+15x-8x-10

⇒3x(4x+5)-2(4x+5)

⇒(4x+5)(3x-2)


(ii) (4-x)2-2x

⇒16+x2-8x-2x

⇒16+x2-10x

⇒x2-10x+16

⇒x2-8x-2x+16

⇒x(x-8)-2(x-8)

⇒(x-8)(x-2)


Question 9

(i) 60x2-70x-30

⇒10(6x2-7x-3)

⇒10(6x2-9x+2x-3)

⇒10(3x(2x-3)+1(2x-3))

⇒10(2x-3)(3x+1)


(ii) x2-6xy-7y2

⇒x2-7xy+xy-7y2

⇒x2(x-7y)+y(x-7y)

⇒(x-7y)(x+y)


Question 10

(i) 2x2+13xy-24y2

⇒2x2+16xy-3xy-24y2

⇒2x(x+8y)-3y(x+8y)

⇒(x+8y)(2x-3y)


(ii) 6x2-5xy-6y2

⇒6x2-9xy+4xy-6y2

⇒3x(2x-3y)+2y(2x-3y)

⇒(2x-3y)(3x+2y)


Question 11

(i) 5x2+17xy-12y2

⇒5x2+20xy-3xy-12y2

⇒5x(x+4y)-3y(x+4y)

⇒(x+4y)(5x-3y)


(ii) x2y2-8xy-48

⇒x2y2-12xy+4xy-48

⇒xy(xy-12)+4(xy-12)

⇒(xy-12)(xy+4)


Question 12

(i) 2a2b2-7ab-30

⇒2a2b2-12ab+5ab-30

⇒2ab(ab-6)+5(ab-6)

⇒(ab-6)(2ab+5)


(ii) a(2a-b)-b2

⇒2a2-ab-b2

⇒2a2-2ab+ab-b2

⇒2a(a-b)+b(a-b)

⇒(a-b)(2a+b)


Question 13

(i) (x-y)2-6(x-y)+5

⇒(x-y)2-5(x-y)-(x-y)+5

⇒(x-y)(x-y-5)-1(x-y-5)

⇒(x-y-5)(x-y-1)


(ii) (2x-y)2-11(2x-y)+28

⇒(2x-y)2-7(2x-y)-4(2x-y)+28

⇒(2x-y)(2x-y-7)-4(2x-y-7)

⇒(2x-y-7)(2x-y-4)


Question 14

(i) 4(a-1)2-4(a-1)-3

⇒4(a-1)2-6(a-1)+2(a-1)-3

⇒2(a-1)(2(a-1)-3)+1(2(a-1)-3)

⇒[2(a-1)-3][2(a-1)+1]

⇒(2a-2-3)(2a-2+1)

⇒(2a-5)(2a-1)


(ii) 1-2a-2b-3(a+b)2

⇒1-2(a+b)-3(a+b)2

⇒1-(a+b)-3(a+b)-3(a+b)2

⇒1(1-(a+b))-3(a+b)(1-(a+b))

⇒(1-3(a+b))(1-(a+b))

⇒(1-3a-3b)(1-a-b)


Question 15

(i) 3-5a-5b-12(a+b)2

⇒3-5(a+b)-12(a+b)2

⇒3-9(a+b)+4(a+b)(1-3(a+b))

⇒3(1-3(a+b))+4(a+b)(1-3(a+b))

⇒(1-3(a+b))(3+4(a+b))

⇒(1-3a-3b)(3+4a+4b)


(ii) a4-11a2+10

⇒a4-10a2-a2+10

⇒a2(a2-10)-1(a2-10)

⇒(a2-10)(a2-1)


Question 16

(i) (x+4)2-5xy-20y-6y2

⇒(x+4)2-5y(x+4)-6y2

⇒(x+4)2-6y(x+4)+y(x+4)-6y2

⇒(x+4)(x+4-6y)+y(x+4-6y)

⇒(x+4-6y)(x+4+y)

⇒(x-6y+4)(x+y+4)


(ii) (x2-2x)2-23(x2-2x)+120

⇒(x2-2x)2-15(x2-2x)-8(x2-2x)+120

⇒(x2-2x)(x2-2x-15)-8(x2-2x-15)

⇒(x2-2x-15)(x2-2x-8)


Question 17

4(2a-3)2-3(2a-3)(a-1)-7(a-1)2

Let 2a-3=x

and a-1=y

∴⇒4x2-3xy-7y2

⇒4x2-7xy+4xy-7y2

⇒x(4x-7y)+y(4x-7y)

⇒(4x-7y)(x+y)

∴Put the value of 2a-3=x and a-1=y

∴(4(2a-3)-7(a-1))(2a-3+a-1)

⇒(8a-12-7a-7)(3a-4)

⇒(a-5)(3a-4)


Question 18

Sol :

(2x2+5x)(2x2+5x-19)+84

Let 2x2+5x=y

then y(y-19)+84

⇒y2-19y+84

⇒y2-12y-7y+84

⇒y(y-12)-7(y-12)

⇒(y-12)(y-7)

Put the value of y=2x2+5x

∴(2x2+5x-12)(2x2+5x-7)

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