find the factors of (i)8x^2yz
(ii)2xy(x+y)
(iii)3x+y^3z
Answers
Answer:
Answer:
(i) 12x = 2 * 2 * 3 * x
36 = 2 * 2 * 3 * 3
Hence, the common factors are 2, 2 and 3 = 2 * 2 * 3 = 12
(ii) 2y = 2 * y
22xy = 2 * 11 * x * y
Hence, the common factors are 2 and y = 2 * y = 2y
(iii) 14pq * 2 * 7 * p * q
28 p2 q2 = 2 * 2 * 7 * p * p * q * q
Hence, the common factors are 2 * 7 * p * q = 14pq
(iv) 2x =2 * x * 1
3x2 = 3 * x * x * 1
4 = 2 * 2 * 1
Hence, the common factors is 1
(v) 6abc = 2 * 2 * a * b * c
24ab2 = 2 * 2 * 3 * a * a *b
12a2 b = 2 * 2 * 3 * a * a * b
Hence, the common factors are 2 * 3 * a * b = 6ab
(vi) 16x3 = 2 * 2 * 2 * 2 * x * x * x
-4x3 = (-1) * 2 * 2 * x * x * x
32x = 2 * 2 * 2 * 2 * 2 * x
Hence, the common factors are 2 * 2 * x = 4x
(vii) 10pq = 2 * 5 * p * q
20qr = 2 * 2 * 5 * q * r
30rp = 2 * 3 * 5 * r * p
Hence, the common factors are 2 * 5 = 10
(viii) 3x2 y3 = 3 * x * x * y * y * y
10x3 y3 = 2 * 5 * x * x * x * y * y * y
6 x2 y2 z = 2 * 3 * x * x * y * y * z
Hence, the common factors are x * x * y * y = x2 y2
Question 2:
Factorize the following expressions.
(i) 7x – 42 (ii) 6p – 12q (iii) 7a2 + 14a (iv) -16z + 20z3 (v) 20l2 m + 30alm
(vi) 5x2 y – 15xy2 (vii) 10a2 – 15b2 + 20c2 (viii) -4a2 + 4ab – 4ca (ix) x2 yz + xy2 z + xyz2
(x) ax2 y + bxy2 + cxyz
Answer:
(i) 7x – 42 = 7 * x – 7 * 6 = 7(x - 6)
(ii) 6p – 12q = 2 * 3 * p – 2 * 2 * 3 * q
= 2 * 3(p – 2 * q)
= 6(p -2q)
(iii) 7a2 + 14a = 7 * a * a + 2 * 7 * a
= 7 * a(a + 2)
= 7a(a + 2)
(iv) -16z + 20z3 = (-1) * 2 * 2 * 2 * 2 * z + 2 * 2 * 5 * z * z * z
= 2 * 2 * z(-2 * 2 + 5 * z * z)
= 4z(-4 + 5z2)
(v) 20l2 m + 30alm = 2 * 2 * 5 * l * l * m + 2 * 3 * 5 * a * l * m
= 2 * 5 * l *m(2 * l + 3 * a)
= 10lm(2l + 3a)