Multiply :
1) (4x2)(5x3)
2) (a2b2c3)(abc2)
3) (0.5a3b)(a2c2)(6b2)
4) 2(3x2 + 5x + 7)
5) 3ab(5a2 + b)
6) 2xy(x2y + xz - xy)
Multiply using Distributive Property.
7) (x + 3)(x - 6)
8) (x + 2)2
9) (3a2 - b)(a2 - 2b)
Multiply :
10) (x + 3)(x2 - 5x + 7)
11) (a + b)(2a2 - 5ab + 3b2)
12) (2x + 3y)(x2 - xy + y2)
Answer (1) :
= (4x2)(5x3)
Group factors with like bases together.
= (4 ⋅ 5)(x2 ⋅ x3)
Use the Product of Powers Property.
= 20x2 + 3
= 20x5
Answer (2) :
= (a2b2c3)(abc2)
Group factors with like bases together.
= (a2 ⋅ a)(b2 ⋅ b)(c3 ⋅ c2)
Use the Product of Powers Property.
= (a2 + 1)(b2 + 1)(c3 + 2)
= (a3)(b3)(c5)
= a3b3c5
Answer (3) :
= (0.5a3b)(a2c2)(6b2)
Group factors with like bases together.
= (0.5 ⋅ 1 ⋅ 6)(a3 ⋅ a2)(b ⋅ b2)c2
Use the Product of Powers Property.
= 3a3 + 2b1 + 2c2
= 3a5b3c2
Answer (4) :
= 2(3x2 + 5x + 7)
Distribute 2.
= 2(3x2) + 2(5x) + 2(7)
Multiply.
= 6x2 + 10x + 14
Answer (5) :
= 3ab(5a2 + b)
Distribute 3ab.
= 3ab(5a2) + 3ab(b)
Group like terms together.
= (3 ⋅ 5)(a ⋅ a2)b + 3a(b ⋅ b)
Use the Product of Powers Property.
= 15a1 + 2b + 3ab1 + 1
= 15a3b + 3ab2
Answer (6) :
= 2xy(x2y + xz - xy)
Distribute 2xy.
= 2xy(x2y) + 2xy(xz) + 2xy(-xy)
Group like terms together.
= 2(x ⋅ x2)(y ⋅ y) + 2(x ⋅ x)yz + 2(-1)(x ⋅ x)(y ⋅ y)
Use the Product of Powers Property.
= 2x1 + 2y1 + 1 + 2x1 + 1yz - 2x1 + 1y1 + 1
= 2x3y2 + 2x2yz - 2x2y2
Answer (7) :
= (x + 3)(x - 6)
Distribute.
= x(x - 6) + 3(x - 6)
Distribute again.
= x(x) + x(-6) + 3(x) + 3(-6)
Multiply.
= x2 - 6x + 3x - 18
Combine like terms.
= x2 - 3x - 18
Answer (8) :
= (x + 2)2
Write as a product of two binomials.
= (x + 2)(x + 2)
Distribute.
= x(x + 2) + 2(x + 2)
Distribute again.
= x(x) + x(2) + 2(x) + 2(2)
Multiply.
= x2 + 2x + 2x + 4
Combine like terms.
= x2 + 4x + 4
Answer (9) :
= (3a2 - b)(a2 - 2b)
Distribute.
= 3a2(a2 - 2b) - b(a2 - 2b)
Distribute again.
= 3a2(a2) + 3a2(-2b) - b(a2) - b(-2b)
Multiply.
= 3a4 - 6a2b - a2b + 2b2
Combine like terms.
= 3a4 - 7a2b + 2b2
Answer (10) :
= (x + 3)(x2 - 5x + 7)
Distributive.
= x(x2 - 5x + 7) + 3(x2 - 5x + 7)
Distribute again.
= x(x2) + x(-5x) + x(7) + 3(x2) + 3(-5x) + 3(7)
Simplify.
= x3 - 5x2 + 7x + 3x2 - 15x + 21
Combine the like terms.
= x3 - 5x2 + 3x2+ 7x - 15x + 21
= x3 - 2x2 - 8x + 21
Answer (11) :
= (a + b)(2a2 - 5ab + 3b2)
Distributive.
= a(2a2 - 5ab + 3b2) + b(2a2 - 5ab + 3b2)
Distribute again.
= a(2a2) + a(-5ab) + a(3b2) + b(2a2) + b(-5ab) + b(3b2)
Simplify.
= 2a3 - 5a2b + 3ab2 + 2a2 b - 5ab2 + 3b3
Combine the like terms.
= 2a3 - 5a2b + 2a2 b - 5ab2 + 3ab2+ 3b3
= 2a3 - 3a2b - 2ab2 + 3b3
Answer (12) :
= (2x + 3y)(x2 - xy + y2)
Distribute.
= 2x(x2 - xy + y2) + 3y(x2 - xy + y2)
Distribute again.
= 2x(x2) +2x(-xy) + 2x(y2) + 3y(x2) + 3y(-xy) + 3y(y2)
Simplify.
= 2x3 - 2x2y + 2xy2 + 3x2y - 3xy2 + 3y3
Combine the like terms.
= 2x3 + x2y - xy2 + 3y3
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