Question

Factor 5x(x + 2)³ + 30y(x + 2).

Option a: 5x(x + 2)(x² + 4x + 4) + 30y
Option b: 5x(x + 2)(x² + 4x + 4y)
Option c: 5x(x + 2)(x² + 4xy + 8)
Option d: 5x(x + 2)(x³ + 6x² + 12x + 8y)

Answer 1

To factor the expression 5x(x + 2)³ + 30y(x + 2), we can first identify the common factor (x + 2) and factor it out. The factored form is 5x(x + 2)(x² + 4x + 4) + 30y.

Step-by-step explanation:

To factor the expression 5x(x + 2)³ + 30y(x + 2), we can first identify the common factor (x + 2). We can factor out (x + 2) from both terms, which gives us:

5x(x + 2)³ + 30y(x + 2) = (x + 2)(5x(x + 2)² + 30y)

Next, we can simplify the expression within the parentheses:

5x(x + 2)² + 30y = 5x(x² + 4x + 4) + 30y

So the factored form of the expression is 5x(x + 2)(x² + 4x + 4) + 30y (Option a).