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) y2−7y+12
=y2−4y−3y+12
=y(y-4)-3(y-4)
=(y-4)(y-3)
(ii) m2−23m+42
=m2−21m−2m+42
=m(m-21)-2(m-21)
=m(m-21)(m-2)
Solution 3
Sol :
(i) y2−5y−24
=y2−8y+3y−24
=y(y-8)+3(y-8)
=(y-8)(y+3)
(ii) t2+23t−108
=t2+27t−4t−108
=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) 14x2−23x+8
=14x2−16x−7x+8
=2 x(7 x-8)-1(7 x-8)
=(7 x-8)(2 x-1)
(ii) 12x2−x−35
=12x2−21x+20x−35
=3 x(42 x-7 x)+5(4 x-7)
=(4 x-7) (3 x+5)
Solution 6
Sol :
(i) 6x2+11x−10
=6x2+15x−4x−10
=3 x(2 x+5)-2(2 x+5)
=(2 x+5)(3 x-2)
(ii) 5−4x−12x2
=5−10x+6x−12x2
=5(1-2 x)+6 x(1-2 x)
=(1-2 x)(5+6 x)
Sol :
(i) 1−18y−63y2
=1−21y+3y−63y2
=1(1-21 y)+3 y(1-21 y)
=(1-21 y)(1+3 y)
(ii) 3x2−5xy−12y2
=3x2−9xy+4xy−12y2
=3 x(x-3 y)+4 y(x-3 y)
=(x-3 y)(3 x+4 y)
Solution 8
Sol :
(i) x2−3xy−40y2
=x2−8xy+5xy−40y2
=x(x-8 y)+5 y(x-8 y)
=(x-8 y)(x+5 y)
(ii) 10p2q2−21pq+9
=10p2q2−15pq−6pq+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+ab−45
=2a2b2+10ab−9ab−45
=2 a b(a b+5)-9(a b+5)
=(a b+5)(2 a b-9)
(ii) x(12x+7)−10
=12x2+7x−10
=12x2+15x−8x−10
=3 x(4 x+5)-2(4 x+5)
=(4 x+5)(3 x-2)
Solution 10
(i) (a+b)2−11(a+b)−42
=(a+b)2−14(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) (x−2y)2−6(x−2y)+5−1×5
=(x−2y)2−5(x−2y)−(x−2y)+5
=(x-2 y)(x-2 y-5)-1(x-2 y-5)
=(x-2 y-5)(x-2 y-1)
(ii) 7+10(2x−3y)−8(2x−3y)20×8=−56
=7+14(2x−3y)−4(2x−3y)−8(2x−3y)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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