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The distributive property is a fundamental principle in algebra that is crucial for simplifying expressions. It allows you to multiply a single term by terms inside parentheses. This property is very useful when dealing with both numerical and algebraic expressions.

Consider the expression \(a(b + c)\). According to the distributive property, you can distribute \(a\) to both \(b\) and \(c\), which gives you \(ab + ac\).

For example, if you have something like \(3(x + 2)\), using distributive property, you multiply \(3\) by \(x\) and \(3\) by \(2\) to get \(3x + 6\).

This is a handy technique when you face expressions where you first need to perform operations inside parentheses before multiplying.

When subtracting decimals, it’s important to align the decimal points to ensure each place value is properly subtracted. This helps in achieving accurate results.

Consider the expression \(5.6 - 6.5\). Here's how you do it correctly:

• Write down the numbers so their decimal points are aligned.
• Subtract from right to left. If necessary, "borrow" from the next left digit.

In our example, \(5.6 - 6.5\) requires us to "borrow," as you cannot subtract 5 from 6 without a negative result, making it \(-0.9\).

This subtraction gives you a negative value because the number you are subtracting is larger than the number you start with.

Multiplying decimals might seem tricky at first, but it's straightforward once broken down into steps. It's just like standard multiplication with a focus on decimal points at the end.

Let's walk through multiplying decimals using \(0.9 \times -0.9\):

• Ignore the decimals temporarily and multiply the whole numbers. Here, you multiply 9 by 9, resulting in 81.
• Count the total number of decimal places in the factors being multiplied. \(0.9\) has one decimal place, and \(-0.9\) has one decimal place, so together, there are two decimal places.
• Place the decimal point in the product. In this example, 81 becomes 0.81 after placing the correct decimal amount.

The final answer is \(-0.81\) as you’ll need to bring the negative sign along with the result found.