Question

Choose the expression(s) that are equivalent to the expression x(x + 1) + x(x + 2).

A) 2x(x + 1)(x + 2)
B) x(2x + 3)
C) x⁴ + 3x²
D) 2x² + 3x
E) X²(x²+3)
F) 4x + 3
G) 7x

Answer 1

The expression x(x + 1) + x(x + 2) simplifies to 2x² + 3x, which is equivalent to option D) 2x² + 3x. Option B) x(2x + 3) is also valid as it represents the expanded form of our simplified expression.

Step-by-step explanation:

The expression given is x(x + 1) + x(x + 2). To find an equivalent expression, we can distribute the x to the terms inside the parentheses in both parts of the expression, resulting in x² + x + x² + 2x. Combining like terms gives us 2x² + 3x, which matches with option D).

Considering other options, none of them match the simplified form of the original expression. For instance, option A) 2x(x + 1)(x + 2) is not equivalent because it results in a cubic polynomial when expanded. Option B) x(2x + 3) is actually the expanded form of the expression we are considering, so it's equivalent to our simplified form and thereby can be considered correct as well. Options C) and E) introduce a power of four and are thus not equivalent. Option F) 4x + 3 and G) 7x are linear expressions and clearly not equivalent to our quadratic expression.