RD Sharma Class 8 Solutions Chapter 7 Factorization Ex 7.2

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RD Sharma Solutions for Class 8 Chapter 7 Factorization Ex 7.2 Download PDF

Factorize the following :

Question 1.
3x-9
Solution:
3x – 9 = 3 (x – 3)        (HCF of 3, 9 = 3)

Question 2.
5x – 15x²
Solution:
5x- 15x² = 5x (1 – 3x)
{HCF of 5, 15 = 5 and of x, x² = x}

Question 3.
20a¹²b² – 15a⁸b⁴
Solution:
20a¹²b² – 15a⁸b⁴
{HCF of 20, 15 = 5, a¹², a⁸ = a⁸, b², b⁴ = b²}
= 5a⁸ b²(4a⁴ – 3b²)

Question 4.
72xy – 96x⁷y⁶
Solution:
72xy – 96x⁷y⁶
HCF of 72, 96 = 24 of x⁶x⁷ = x⁶, y⁷,y⁶ = y⁶
∴ 72x⁷y⁶ – 96x⁷y⁶ = 24x⁶y⁶ (3y – 4x)

Question 5.
20X³ – 40x² + 80x
Solution:
20x³ – 40x² + 80x
HCF of 20, 40,80 = 20
HCF of x³, x², x = x
∴ 20x³ – 40x² + 80x = 20x (x² – 2x + 4)

Question 6.
2x³y² – 4x²y³ + 8xy⁴
Solution:
2x³y² – 4x²y³ + 8xy⁴
HCF of 2, 4, 8 = 2
HCF of x³, x², x = 1
and HCF of y², y³, y⁴ = y²
∴ 2x³y² – 4x²y³ + 8xy⁴
= 2xy² (x² – 2xy + 4y²)

Question 7.
10m³n² + 15m⁴n – 20m²n³
Solution:
10m³n² + 15m⁴n – 20m²n³
HCF of 10, 15, 20 = 5
HCF of m³, m⁴, m² = m²
HCF of n², n, n³ = n
10m³n² + 15m⁴n – 20m²n³
5m²n(2mn + 3m²– 4n²)

Question 8.
2a⁴b⁴ – 3a³b⁵ + 4a²b⁵
Solution:
2a⁴b⁴ – 3a³b⁵ + 4a²b⁵
HCF of 2, 3, 4= 1
HCF of a⁴, a³, a² = a²
HCF of b⁴, b⁵ b⁵ = b⁴
∴ 2a⁴b⁴ – 3a³b⁵ + 4a²b⁵ = a²b⁴
(2a² – 3ab + 4b)

Question 9.
28a² + 14a²b² – 21a⁴
Solution:
28a² + 14a²b² – 21a⁴
HCF of 28, 14,21 =7
HCF of a², a², a⁴ = a²
HCF of 1, b², 1 = 1
∴ 28a² + 14a²b²-21a⁴ = 7a²
(4 + 2b² – 3a²)

Question 10.
a⁴b – 3a²b² – 6ab³
Solution:
a⁴b – 3a²b² – 6ab³
HCF of 1,3,6 = 1
HCF of a⁴, a², a = a
HCF of b, b², b³ = b
∴ a⁴b – 3a²b² – 6ab³ = ab (a³ – 3ab – 6b²)

Question 11.
2l²mn – 3lm²n + 4lmn²
Solution:
2l²mn – 3lm²n + 4lmn²
HCF 2, 3,4 = 1,
HCF of l²,l,l = l
HCF of m, m², m = m
HCF of n, n, n² = n
∴ 2l² mn – 3lm²n + 4lmn²
= lmn (21 -3m + 4n)

Question 12.
x⁴y² – x²y⁴ – x⁴y⁴
Solution:
x⁴y² – x²y⁴ – x⁴y⁴
HCF of x⁴, x², x⁴ = x²
HCF of y², y⁴, y⁴ =y²
∴ x⁴y² – x²y⁴ – x⁴y⁴ = x²y² (x² -y² -x²y²)

Question 13.
9 x²y + 3 axy
Solution:
9 x²y + 3 axy
HCF of 9, 3 = 3
HCF of x², x = x
HCF of y,y = y
HCF of 1,a = 1
∴ 9x²y + 3axy = 3xy (3x + a)

Question 14.
16m – 4m²
Solution:
16m – 4m²
HCF of 16, 4 = 4
HCF of m, m² = m
∴ 16m – 4m² = 4m (4 – m)

Question 15.
-4a² + 4ab – 4ca
Solution:
-4a² + 4ab – 4ca
HCF of 4, 4, 4 = 4
HCF of a², a, a = a
∴ -4a² + 4ab – 4ca = -4a (a – b + c)

Question 16.
^{x2yz + xy2z + xyz2}
Solution:
x²yz + xy²z + xyz²
HCF of x², x, x = x
HCF of y,y²,y=y
HCF of z, z,z² = z
∴ x²yz + xy²z + xyz² = xyz (x + y + z)

Question 17.
ax²y + bxy² + cxyz
Solution:
ax²y + bxy² + cxyz
HCF of x², x, x = x,
HCF of y,y²,y = y
ax²y + bxy² + cxyz = xy (ax + by + cz)

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