Question

write the expanded form of the expression.
-1.5(-3 + 4n + 8.2)
-1.5(-3 + 4n + 8.2)=square
(use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Apply the distributive property

The distributive property states that \(a(b + c + d)=ab+ac + ad\). So for \(-1.5(-3 + 4n+8.2)\), we distribute \(-1.5\) to each term inside the parentheses.
\(-1.5\times(-3)+(-1.5)\times(4n)+(-1.5)\times(8.2)\)

Step2: Calculate each product

• Calculate \(-1.5\times(-3)\): Multiplying two negative numbers gives a positive number, so \(-1.5\times(-3) = 4.5\)
• Calculate \(-1.5\times(4n)\): Multiply the coefficients, so \(-1.5\times4n=-6n\)
• Calculate \(-1.5\times(8.2)\): Multiplying a negative and a positive number gives a negative number, and \(1.5\times8.2 = 12.3\), so \(-1.5\times8.2=-12.3\)

Step3: Combine the terms

Now we combine the results from step 2: \(4.5-6n - 12.3\)
Then combine the constant terms \(4.5-12.3=-7.8\)
So the expanded form is \(-6n-7.8\)

Answer:

\(-6n - 7.8\)