NCERT Solution For Class 8 Math Chapter 14 Exercise 14.1 Factorisation
1. Find the common factors of the giving terms.
(i) 12x , 36
Ans
12x = 2*2*3*x
36 = 2*2*3*3
Common factors = 2*2*3 = 12
(ii) 2y , 22xy
Ans
2y = 2*y
22xy = 2*11*x*y
Common factors = 2*y = 2y
iii) 14pq, 28p2q2
Ans
14pq=2x7xpxq
28p2q2 =2x2x7xpxpxqxq
Common factors = 2*7*p*q= 14pq.
iv) 2x, 3x², 4
Ans
2x=2*x
3x² = 3*x*x
4 = 2*2
Common factors of 2x, 3x7 and 4 is 1.
v) 6abc, 24ab2, 12a2b
Ans
6abc2×3×a×bxc
24ab2=2×2×2×3*a*b*b
12a b=2×2×3×a×a×b
Common factors of 6abc, 24ab2 and 12a2b are 2, 3, a and b = 2x3xa*b=6ab.
vi) 16x³, -4x², 32x
Sol:-
16x3=2*2*2*2*x*x*x
-4x²= -2*2*x*x
32x = 2*2*2*2*2*x
Common factors of 6x-4x2 and 32x are 2, 2 and x = 2*2*x = 4x.
vi) 10pq, 20gr, 30rp
Ans
10pq=2*5*p*q
20qr = 2*2*5*q*г
30rp = 2*3*5*r*p
Common factors of 10pq, 20qr and 30rp are 2 and 5 = 2*5=10.
viii) 3x2y³, 10x³y2, 6x2y2z
Ans
3x²y = 3*Ñ…*Ñ…*у
10x³y² = 2*5*x*x*x*y*y
6x2y2z = 2*3*x*x*y*y*z
Common factors of 3x2y2, 10xy2 and 6x y z are x, x, y and y = x*x*y*y = x²y2.
2. Factorise the following expressions.
i) 7x - 42
Sol.:
7x-42
= 7x - 7 * 2 * 3
= 7(x - 2 * 3)
= 7(x - 6)
ii) 6p - 12q
Sol.:
6p - 12q = 2 * 3p - 2 * 2 * 3q
= 2 * 3(p - 2q)
= 6(p - 2q)
iii) 7a ^ 2 + 14a
Sol.:
= 7*a*a + 2 * 7*a
= 7*a (a+2)
= 7a(a+2)
iv)-16z +20z
Sol:
16z+20z3
=-2×2×2×2×z + 2×2*5*z*z*z
= 2x2xz (-2x2 + 5xzxz)
= 42(-4+5z2)
v) 20 L ^ 2m + 30 alm
Sol:
201m+30 alm
= 2×2×5*1*1*m+2×3×5xaxlxm
=2x5x1xm (2x1+3xa)
= 10lm (21+3a)
vi) 5x^2y-15xy2
Sol:
5x2y-15xy2
= 5*x*x*y - 3×5*x*y*y
= 5*x*y (x -3xy)
= 5xy(x-3y)
vii) 10a2-15b2+20c2
Sol:
10a-15b2+20c2
= 2*5*a*a - 3×5xbxb + 2x2x5xcxc
= 5 (2xaxa - 3xbxb + 2x2xcxc)
5(2a^2-3b^2+ 4c²)
viii)-4a2+ 4ab - 4ca
Sol..
4a²+4ab4ca = -2x2xaxa + 2*2*a*b-2*2*c*a
= 2x2xa(-a+b-c)
= 4a(-a + b - c)
ix) x²yz + xy²z + xyz²
Sol.:
x²yz + xy z + xyz2
= xxxxyxz + xxyxyxz + xxyxzxz
= xxyxz (x + y + z)
= xyz (x + y + z)
x) ax²y + bxy² + cxyz
Sol.
ax2y+ bxy2+ cxyz
= a*x*x*y + b*x*y*y + c*x*y*z
= x*y (a*x + b*y + c*z)
= xy (ax + by + cz)
3. Factorise
i) x ^ 2 + xy + 8x + 8y
Sol:-
x²+ xy +8x + 8y
= x(x + y) + 8(x + y)
(x + 8)(x + y)
ii) 15xy - 6x + 5y - 2
Sol.:-
15xy-6x+5y - 2
= 3x(5y - 2) + 1(5y - 2)
(3x + 1)(5y - 2)
iii) ax + bx - ay - by
Sol.: -
ax + bx - ay - by
= x(a + b) - y(a + b)
= (x - y)(a + b)
iv) 15pq + 15 + 9q + 25p
Sol.:-
15pq+15+9q+25p
- 15pq + 25p + 9q + 15
= 5p(3q + 5) + 3(3q + 5)
= (5p + 3)(3q + 5)
v) z - 7 + 7xy - xyz
Sol.: -
z-7+7xy - xyz
= 1(z - 7) + xy (7-z)
= 1(z-7) - xy(z - 7)
= (z - 7) (1 - xy)
.