Question

1. which expression is equivalent to $2x(y^2 + 3) - 5(3 + y^2)$?

a. $(2x - 5)(3 + y^2)$
b. $2x(3y^2) - 5(3y^2)$
c. $(2x + 3) - (5 + y^2)$
d. $(2x + 5)(y^2 + 3)$

Explanation:

Step1: Identify common factor

Notice that both terms \(2x(y^2 + 3)\) and \(-5(3 + y^2)\) have a common factor of \((y^2 + 3)\) (since \(3 + y^2=y^2 + 3\)).

Step2: Apply distributive property (factoring)

Using the distributive property of multiplication over subtraction, \(ab - ac=a(b - c)\), where \(a=(y^2 + 3)\), \(b = 2x\), and \(c = 5\). So we can factor out \((y^2+3)\) from the expression \(2x(y^2 + 3)-5(3 + y^2)\) to get \((2x - 5)(3 + y^2)\) (because \(3 + y^2=y^2 + 3\)).

Answer:

A. \((2x - 5)(3 + y^2)\)