Question

integer operations quiz
simplify the following by using distribution:
-6 (2x + 5y - 1)
○ -42xy + 6
○ -36xy
○ -12x - 30y + 6
○ 12x + 30y - 6

Explanation:

Step1: Apply distributive property

The distributive property states that \(a(b + c + d)=ab+ac + ad\). Here, \(a=-6\), \(b = 2x\), \(c = 5y\), \(d=-1\). So we multiply \(-6\) with each term inside the parentheses:
\(-6\times(2x)+(-6)\times(5y)+(-6)\times(-1)\)

Step2: Calculate each product

• For \(-6\times(2x)\): Multiply the coefficients \(-6\) and \(2\) to get \(-12\), so \(-6\times(2x)=-12x\).
• For \(-6\times(5y)\): Multiply the coefficients \(-6\) and \(5\) to get \(-30\), so \(-6\times(5y)=-30y\).
• For \(-6\times(-1)\): Multiplying two negative numbers gives a positive number, so \(-6\times(-1) = 6\).

Combining these results, we get \(-12x-30y + 6\).

Answer:

\(-12x - 30y + 6\) (corresponding to the option: \(-12x - 30y + 6\))