Algebraic expressions can look complex, especially if you’re new to the topic. However, once you understand how to calculate the value of an algebraic expression, you’ll find it much simpler to tackle. In this article, we’ll take a closer look at how to calculate the value of an algebraic expression.

To begin with, we need to understand what an algebraic expression is. An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. A variable is a letter that represents a number, while constants are fixed quantities that do not change.

Before we can calculate the value of an algebraic expression, we need to know the values of the variables. For example, consider the expression 3x + 4. If we know the value of x is 2, we can substitute 2 for x in the expression to get 3(2) + 4, which equals 10. Therefore, the value of the expression when x is equal to 2 is 10.

Now let’s consider a more complex expression, such as 2x² + 3x – 4. To calculate the value of this expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division from left to right, and finally addition and subtraction from left to right.

In this expression, we do not have any parentheses or exponents, so we move to the multiplication and division. However, we don’t have any multiplication or division signs, so we move to the addition and subtraction. We add 2x² to 3x, which gives us 2x² + 3x. Finally, we subtract 4 from this result to get 2x² + 3x – 4.

At this point, we still do not have the value of the expression because we do not know the value of x. Let’s say that x is equal to 5. We can substitute 5 for x in the expression to get 2(5)² + 3(5) – 4, which simplifies to 50 + 15 – 4, which equals 61. Therefore, the value of the expression when x is equal to 5 is 61.

Sometimes, we may need to simplify an expression before we can calculate its value. For example, consider the expression (4x – 3)(2x + 5). To simplify this expression, we need to use the distributive property, which states that a(b + c) is equal to ab + ac. Applying this property, we get:

(4x – 3)(2x + 5) = 4x(2x) + 4x(5) – 3(2x) – 3(5)
= 8x² + 20x – 6x – 15
= 8x² + 14x – 15

Now that we’ve simplified the expression, we can calculate its value. Let’s assume that x is equal to 2. Substituting 2 for x in the expression, we get 8(2)² + 14(2) – 15, which simplifies to 39. Therefore, the value of the expression when x is equal to 2 is 39.

In conclusion, calculating the value of an algebraic expression involves substituting the values of the variables and following the order of operations. It may also involve simplifying the expression before calculating its value. With practice, you’ll find that calculating the value of an algebraic expression becomes second nature.

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