ML Aggarwal Solution Class 9 Chapter 4 Factorisation Exercise 4.2

 Exercise 4.2

Question 1

(i) x2+xy-x-y

⇒x2+xy-(x+y)

⇒x(x+y)-1(x+y)

⇒(x+y)(x-1)


(ii) y2-yz-5y+5z

⇒y(y-z)-5(y-z)

⇒(y-z)(y-5)


Question 2

(i) 5xy+7y-5y2-7x

⇒5xy-7x+7y-5y2

⇒x(5y-7)+y(7-5y)

⇒x(5y-7)-y(5y-7)

⇒(5y-7)(x-y)


(ii) 5p2-8pq-10p+16q

⇒p(5p-8q)-2(5p-8q)

⇒(5p-8q)(p-2)


Question 3

(i) a2b-ab2+3a-3b

⇒ab(a-b)+3(a-b)

⇒(a-b)(p-2)


(ii) x3-3x2+x-3

⇒x2(x-3)+1(x-3)

⇒(x-3)(x2+1)


Question 4

(i) 6xy2-3xy-10y+5

⇒3xy(2y-1)-5(2y-1)

⇒(2y-1)(3xy-5)


(ii) 3ax-6ay-8by+4bx

⇒3a(x-2y)-4b(2y-x)

⇒3a(x-2y)+4b(x-2y)

⇒(x-2y)(3a+4b)


Question 5

(i) 1-a-b+ab

⇒(1-a)1-b(1-a)

⇒(1-a)(1-b)


(ii) a(a-2b-c)+2bc

⇒a2-2ab-ac+2bc

⇒a(a-2b)-c(a-2b)

⇒(a-2b)(a-c)


Question 6

(i) x2+xy(1+y)+y3

⇒x2+xy+xy2+y3

⇒x(x+y)+y2(x+y)

⇒(x+y)(x+y2)


(ii) y2-xy(1-x)-x3

⇒y2-xy+x2y-x3

⇒y(y-x)+x2(y-x)

⇒(y-x)(y+x2)


Question 7

(i) ab2+(a-1)b-1

⇒ab2+ab-b-1

⇒ab(b+1)-1(b+1)

⇒(b+1)(ab-1)


(ii) 2a-4b-xa+2bx

⇒2(a-2b)-x(a-2b)

⇒(a-2b)(2-x)


Question 8

(i) 5ph-10qk+2rph-4qr

⇒5ph+2rph-10qk-4qrk

⇒ph(5+2r)-2qk(5+2r)

⇒(5+2r)(ph-2qk)


(ii) x2-x(a+2b)+2ab

⇒x2-ax-2xb+2ab

⇒x(x-a)-2b(x-a)

⇒(x-a)(x-2b)


Question 9

(i) ab(x2+y2)-xy(a2+b2)

⇒abx2+aby2-a2xy-b2xy

⇒abx2-b2xy+aby2-a2xy

⇒bx(ax-by)-ay(ax-by)

⇒(ax-by)(bx-ay)


(ii) (ax+by)2+(bx-ay)2

⇒(ax)2+(by)2+2.ax.by+(bx)2+(ay)2-2.bx.ay

⇒a2x2+b2y2+b2x2+a2y2

⇒a2x2+a2y2+b2y2+b2x2

⇒a2(x2+y2)+b2(x2+y2)

⇒(x2+y2)(a2+b2)


Question 10

(i) a3+ab(1-2a)-2b2

⇒a3+ab-2a2b-2b2

⇒a3-2a2b+ab-2b2

⇒a2(a-2b)+b(a-2b)

⇒(a-2b)(a2+b)


(ii) 3x2y-3xy+12x-12

⇒3xy(x-1)+12(x-1)

⇒(x-1)(3xy+12)


Question 11

a2b+ab2-abc-b2c+axy+bxy

⇒a2b-abc+axy+ab2-b2c+bxy

⇒a(ab-bc+xy)+b(ab-bc+xy)

⇒(a+b)(ab-bc+xy)


Question 12

ax2-bx2+ay2-by2+az2-bz2

⇒ax2+ay2+az2-bx2-by2-by2-bz2

⇒a(x2+y2+z2)-b(x2+y2+z2)

⇒(x2+y2+z2)(a-b)


Question 13

x-1-(x-1)2+ax-a

⇒x-1-(x2+1-2x)+ax-a

⇒x-1-x2-1+2x+ax-a

⇒2x-x2+ax-2+x-a

⇒x(2-x+a)-1(2-x+a)

⇒(2-x-a)(x-1)

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