Problem 37 - Algebra 2

Question

Evaluate each expression for \(a=3\) and \(b=-5\). \(-4+2 a b\)

Step-by-Step Solution

Answer

-34

Step 1: Substitute the values of a and b

Replace the variables 'a' and 'b' with their respective values in the expression. Given that: \(a=3\) and \(b=-5\), the expression \(-4+2ab\) becomes \(-4+2(3)(-5)\).

Step 2: Simplify the multiplication

Multiply the numbers 2, 3, and -5 together. The multiplication part of the expression \(2 \times 3 \times -5\) simplifies to \(-30\).

Step 3: Subtract to find the final result

Subtract -30 from -4 to get the evaluation of the expression. This involves adding a negative number to a negative number, which is \(-4 - 30 = -34\).

Key Concepts

Substitution Method

The substitution method is an essential technique in algebra, particularly when evaluating algebraic expressions. It involves replacing variables with their corresponding numerical values. For example, let's consider the exercise where you're given the expression -4+2ab to evaluate for a=3 and b=-5.

To apply the substitution method, follow these steps:

• Identify the variables in the expression. In this case, a and b.
• Replace each variable with the given number, which translates to a=3 and b=-5.
• Substitute these values into the expression, which gives us -4+2(3)(-5).

By substituting the values, we can work with actual numbers rather than abstract symbols, which simplifies the process of solving the expression.

Simplifying Expressions

Simplifying expressions is the process of reducing an expression to its most basic form. This is done by performing arithmetic operations and combining like terms where possible. Referencing our example expression -4+2ab, after substituting a and b with 3 and -5, respectively, we obtain -4+2(3)(-5).

Here's how to simplify the expression:

• Carry out the multiplication operation first, according to the order of operations (PEMDAS/BODMAS). This gives you -4+(6)(-5), which simplifies further to -4-30.
• Add or subtract the numbers to combine them into a single value, resulting in -34 for the final simplified form of the expression.

Simplifying an expression makes it easier to understand and work with, especially when dealing with more complex algebraic problems.

Arithmetic Operations in Algebra

Understanding arithmetic operations in algebra is crucial for evaluating expressions. These operations include addition, subtraction, multiplication, and division. In algebra, these operations follow the same fundamental rules as in regular arithmetic, but they also involve working with variables.

Let's discuss the arithmetic operations within the context of our example expression -4+2ab. With the substituted values, the expression becomes -4+2(3)(-5).

To correctly evaluate this expression, we follow the order of operations:

• Multiplication first: 2 * 3 * -5 equates to -30.
• Addition or subtraction next: combining -4 and -30 results in -34.

Remembering the order of operations ensures that you solve algebraic expressions accurately and arrive at the correct results.