Question

Remove the brackets from the given expression: $(-2)(a+b)$

Short answer

Question: Remove the brackets from the expression $(-2)(a+b)$ and simplify. Answer: The simplified expression without brackets is $-2a-2b$.

Step-by-step solution

Understand the Distributive Property

The Distributive Property states that given an expression of the form $c(a+b)$, we can distribute $c$ to both terms inside the parentheses: $c(a+b)=c\cdot a+c\cdot b$.

Apply the Distributive Property

Now apply the Distributive Property to the given expression $(-2)(a+b)$: $(-2)(a+b)=(-2)\cdot a+(-2)\cdot b$.

Simplify the Expression

Simplify the expression from Step 2: $(-2)\cdot a+(-2)\cdot b=-2a-2b$. Hence, the simplified expression without brackets is $-2a-2b$.

Key concepts

Removing Brackets in Algebra

The concept of removing brackets in algebra is an essential part of simplifying mathematical expressions. It involves the process of eliminating parentheses from an equation or expression, paving the way to a simpler form. This technique is particularly useful, as it allows you to see the components of algebraic expressions more clearly, and is a crucial step in solving more complex problems.

For example, if you encounter an expression like , removing the brackets involves multiplying each term inside the brackets by the factor outside, resulting in . This is the foundational step and is often followed by combining like terms if applicable. Remember, if there's a negative sign before the brackets, like in our original exercise , each term inside the brackets gets multiplied by , flipping the sign of each term accordingly.

Simplifying Algebraic Expressions

Simplifying algebraic expressions is a process that combines several steps, including removing brackets, like we just discussed, and then combining like terms to condense the expression into its most compact form. The aim is to make the expression as straightforward as possible without changing its value.

Let's take the expression as an example. To simplify this, we would combine the like terms which are terms that have the exact same variable raised to the same power. So for the x terms, we combine and to get , and for the numerical terms, we combine and to get . The expression thus simplifies to . It's a straightforward process, but it takes careful attention to correctly combine and reduce terms.

Applying the Distributive Property

The Distributive Property is a fundamental algebraic property that allows us to multiply a number or expression by a sum or difference inside brackets. Formally, it's stated as . This means you distribute the multiplication of across each term inside the brackets to and respectively.

Let's use this property in an example. Given the expression , applying the Distributive Property, you would get . It's a simple yet powerful tool in algebra. Notice how it streamlines the process of removing brackets, essentially combining two steps into one, and sets the stage for any further simplification required in solving algebraic equations. Remember to distribute the sign before the brackets as well, as it's a common mistake to lose the sign during simplification.