Question

which expressions are equivalent to 5x - 8x + 12y? (choose 3)
a 3(x - 4y)
b 3(-x + 4y)
c -3x + 12y
d -3(x - 4y)
e -3(-x + 4y)

Explanation:

Step1: Simplify the original expression

First, combine like terms in \(5x - 8x + 12y\). The like terms for \(x\) are \(5x\) and \(-8x\). So, \(5x - 8x = -3x\). Thus, the original expression simplifies to \(-3x + 12y\).

Step2: Analyze Option A

Simplify \(3(x - 4y)\) using the distributive property: \(3\times x - 3\times 4y = 3x - 12y\). This is not equivalent to \(-3x + 12y\), so A is incorrect.

Step3: Analyze Option B

Simplify \(3(-x + 4y)\) using the distributive property: \(3\times(-x) + 3\times 4y = -3x + 12y\). This matches the simplified original expression, so B is correct.

Step4: Analyze Option C

The expression \( -3x + 12y\) is exactly the simplified form of the original expression, so C is correct.

Step5: Analyze Option D

Simplify \(-3(x - 4y)\) using the distributive property: \(-3\times x - 3\times(-4y) = -3x + 12y\). This matches the simplified original expression, so D is correct.

Step6: Analyze Option E

Simplify \(-3(-x + 4y)\) using the distributive property: \(-3\times(-x) + -3\times 4y = 3x - 12y\). This is not equivalent to \(-3x + 12y\), so E is incorrect.

Answer:

B. \(3(-x + 4y)\)
C. \(-3x + 12y\)
D. \(-3(x - 4y)\)