Question

Which of these is a correct expansion of (3x−2)(2x²+5)?

A. 3x⋅2x²+3x⋅5+(−2)⋅2x²+(−2)⋅5
B. 3x⋅2x²+3x⋅5+2⋅2x²+2⋅5
C. 3x⋅2x²+(−2)⋅2x²+2x²⋅5+(−2)⋅5

Answer 1

The correct expansion of the expression (3x−2)(2x²+5) is option A, which simplifies to 6x³ + 15x - 4x² - 10 by applying the distributive property. Applying these rules leads us to the correct expanded form as in option A.

Step-by-step explanation:

To find the correct expansion of the given expression (3x−2)(2x²+5), we apply the distributive property of multiplication over addition.

This property states that a(b + c) = ab + ac. We need to multiply each term in the first parentheses by each term in the second parentheses.

The correct expansion is therefore:
A. 3x⋅ 2x² + 3x⋅ 5 + (−2)⋅ 2x² + (−2)⋅ 5

This can further be simplified to: 6x³ + 15x - 4x² - 10.

According to the multiplication rules for signs:

• When two positive numbers multiply, the answer has a positive sign.
• When two negative numbers multiply, the answer has a positive sign.
• When two numbers with opposite signs multiply, the answer has a negative sign.

Applying these rules leads us to the correct expanded form as in option A.