ML AGGARWAL CLASS 8 CHAPTER 11 Factorisation Exercise 11.4

 Exercise 11.4

Solution 1

Sol :
(i) x2+3x+2

x2+2x+x+2

x(x+2)+1(x+2)

(x+1)(x+2)


(ii) z2+10z+24

=z2+6z+4z+24

=z(z+6)+4(z+6)

=(z+6)(z+4)



Solution 2

Sol :
(i) y27y+12

=y24y3y+12

=y(y-4)-3(y-4)

=(y-4)(y-3)


(ii) m223m+42

=m221m2m+42

=m(m-21)-2(m-21)

=m(m-21)(m-2)



Solution 3

Sol :
(i) y25y24

=y28y+3y24

=y(y-8)+3(y-8)

=(y-8)(y+3)


(ii) t2+23t108

=t2+27t4t108

=t(t+27)-4(t+27)

=(t+27)(t-4)


Solution 4

Sol :
(i) 3x2+14x+8

=3x2+12x+2x+8

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

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


(ii) 3y2+10y+8

=3y2+6y+4y+8

=3 y(y+2)+4(y+2)

=(y+2)(3 y+4)


Solution 5

Sol :
(i) 14x223x+8

=14x216x7x+8

=2 x(7 x-8)-1(7 x-8)

=(7 x-8)(2 x-1)


(ii) 12x2x35

=12x221x+20x35

=3 x(42 x-7 x)+5(4 x-7)

=(4 x-7) (3 x+5)


Solution 6

Sol :
(i) 6x2+11x10

=6x2+15x4x10

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

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


(ii) 54x12x2

=510x+6x12x2

=5(1-2 x)+6 x(1-2 x)

=(1-2 x)(5+6 x)
 

Solution 7

Sol :
(i) 118y63y2

=121y+3y63y2

=1(1-21 y)+3 y(1-21 y)

=(1-21 y)(1+3 y)


(ii) 3x25xy12y2

=3x29xy+4xy12y2

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

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

 
Solution 8

Sol :
(i) x23xy40y2

=x28xy+5xy40y2

=x(x-8 y)+5 y(x-8 y)

=(x-8 y)(x+5 y)

 
(ii) 10p2q221pq+9

=10p2q215pq6pq+9

=5 p q(2 p q-3)-3(2 p q-3)

=(2 p q-3)(5 p q-3)



Solution 9

Sol :
(i) 2a2b2+ab45

=2a2b2+10ab9ab45

=2 a b(a b+5)-9(a b+5)

=(a b+5)(2 a b-9)


(ii) x(12x+7)10

=12x2+7x10

=12x2+15x8x10

=3 x(4 x+5)-2(4 x+5)

=(4 x+5)(3 x-2)



Solution 10


(i) (a+b)211(a+b)42

=(a+b)214(a+b)+3(a+b)42

=(a+b)(a+b-14)+3(a+b-14)

=(a+b-14)(a+b+3)


(ii) 8+6(p+q)5(p+q)2

=8+10(p+q)4(p+q)5(p+a)2

=2(4+5(p+q))-(p+q)(4+5(p+a))

=(4+5(p+q))(2-(p+q))


Solution 11

Sol :
(i) (x2y)26(x2y)+51×5

=(x2y)25(x2y)(x2y)+5

=(x-2 y)(x-2 y-5)-1(x-2 y-5)

=(x-2 y-5)(x-2 y-1)


(ii) 7+10(2x3y)8(2x3y)20×8=56

=7+14(2x3y)4(2x3y)8(2x3y)2

=7(1+2(2 x-3 y))-4(2 x-3 y)(1+2(2 x-3 y))

=(1+2(2 x-3 y))(7-4(2 x-3 y))

=(1+4 x-6 y)(7-8 x+12 y)

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