MULTIPLYING MONOMIAL AND BINOMIAL

Problem 2 :

9y² (5y - 3)

Solution :

= 9y² (5y - 3)

Distribute 9y²,

= 9y² (5y) + 9y² (-3)

Combine the like terms,

= 45y³ - 27y²

Problem 3:

y(y + 5)

Solution :

= y(y + 5)

Distribute y,

= y(y) + y(5)

Combine the like terms,

= y² + 5y

Problem 4 :

-2n (7 – 5n²)

Solution :

= -2n (7 – 5n²)

Distribute -2n,

= -2n(7) – 2n(-5n²)

Combine the like terms,

= -14n + 10n³

Problem 5 :

-2v⁷ (15v⁶ + 46v⁴)

Solution :

= -2v⁷ (15v⁶ + 46v⁴)

Distribute -2v⁷,

= -2v⁷ (15v⁶) - 2v⁷ (46v⁴)

Combine the like terms,

= -30v⁷⁺⁶ - 92v⁷⁺⁴

= -30v¹³ – 92v¹¹

Problem 6 :

1/9 a² (81a⁵ - 72)

Solution :

= 1/9 a² (81a⁵ - 72)

Distribute 1/9 a²,

= 1/9 a² (81 a⁵) – 1/9 a² (72)

Combine the like terms,

= 9a⁷ – 8a²

Problem 7 :

-4m⁶ (-7m³ + 5m⁶)

Solution :

= -4m⁶ (-7m³ + 5m⁶)

Distribute -4m⁶,

= -4m⁶(-7m³) – 4m⁶(5m⁶)

Combine the like terms,

= 28m⁶⁺³ – 20m⁶⁺⁶

= 28m⁹ – 20m¹²

Problem 8 :

r⁵ (-3r – 8r⁴)

Solution :

= r⁵ (-3r – 8r⁴)

Distribute r⁵,

= r⁵(-3r) + r⁵(-8r⁴)

Combine the like terms,

= -3r⁵⁺¹ – 8r⁵⁺⁴

= -3r⁶ – 8r⁹

Problem 9 :

13z⁴ (6z⁷ + 4z⁵)

Solution :

= 13z⁴ (6z⁷ + 4z⁵)

Distribute 13z⁴

= 13z⁴ (6z⁷) + 13z⁴ (4z⁵)

Combine the like terms,

= 78z⁴⁺⁷ + 52z⁴⁺⁵

= 78z¹¹ + 52z⁹

Problem 10 :

-28d³ (-5/28 d² - 2/7 d)

Solution : 

= -28d³ (-5/28 d² - 2/7 d)

Distribute -28d³

= -28d³ (-5/28 d²) – 28d³(-2/7 d)

Combine the like terms,

= 5d³⁺² + 4d³⁺¹

= 5d⁵ + 4d⁴