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Algebraic expressions are a collection of terms connected by operations such as multiplication, division, addition, subtraction, exponents, and more.
The order of operations goes:
1.Parentheses
2.Exponents
3.Multiplication
4.Division
5.Addition
6. Subtraction
This is commonly remembered using the accronym PEMDAS.
Almost every problem in math will contain some algebraic expressions, and you have probably seen them before. In this lesson, you will learn how to break them down and evaluate them.
Give all of the operations in order that occur in the expression \(\sqrt{3x^2+1}\), then evaluate it at \(x = 4\)
Operations:
The first operation in PEMDAS, is Parentheses, which means that what is inside a parenthesis must be evaluated first. Because the square root is around the \(3x^2+1\), it acts like a parenthesis, which means that \(3x^2+1\) is evaluated before we take its square root. In PEMDAS, exponents come before multiplication, which is before addition, therefor the answer is:
1. \(x\) is squared
2.\(x^2\) is multiplied by \(3\)
3. \(1\) is added \(3x^1\)
4. We take the square root of \(3x^2+1\)
Now we know how to evauluate \(\sqrt{3x^2+1}\) at \(x=4\). First we square x to get \(16\). Next, we multiply this by \(3\) to get \(48\). Next we add \(1\) to get \(49\), and finally we take the square root to get \(7\)
Evaluate the expression \(\frac{4x^2+9}{3x-4}\) at x = 3
Note: Here the numerator and denominator act as expressions in parentheses so we have to evaluate each individually before we divide.
$$\frac{4x^2+9}{3x-4}$$
$$=\frac{4*3^2+9}{3*3-4}$$
$$=\frac{4*9+9}{9-4}$$
$$=\frac{36+9}{5}$$
$$=\frac{45}{5}$$
$$=9$$
Conlcusion:
In these problems, it is important to remember hidden parentheses created by things like square roots and fractions, that include multiple terms.