Question

polynomials operations - review for test#2 (adding, subtracting, multiplying) which expression is equivalent to 2.5(2x - 8y) - 4(2.5x - 8y)? -5x - 12y -5x + 12y 5x - 12y 5x + 12y

Explanation:

Step1: Expand the first term

Multiply \(2.5\) with \((2x - 8y)\): \(2.5\times2x - 2.5\times8y = 5x - 20y\)

Step2: Expand the second term

Multiply \(4\) with \((2.5x - 8y)\): \(4\times2.5x - 4\times8y = 10x - 32y\)

Step3: Subtract the two expanded terms

\((5x - 20y)-(10x - 32y)=5x - 20y - 10x + 32y\)

Step4: Combine like terms

Combine \(x\) terms: \(5x - 10x=-5x\)
Combine \(y\) terms: \(-20y + 32y = 12y\)
So the result is \(-5x + 12y\)

Answer:

\(-5x + 12y\) (corresponding to the option \(-5x + 12y\))