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Simplifying expressions means making them as simple as possible. This usually means performing all possible arithmetic operations and combining like terms. For instance, consider the expression \[2x + x^2 \] To simplify this, you substitute the value of x into the expression. Let's use x = 4 as an example. When we substitute, we get: \[2(4) + 4^2 \] Then, perform the calculations step-by-step: \[2(4) = 8 \] and \[4^2 = 16 \] Finally, add these results: \[8 + 16 = 24 \] Now the expression is simplified to 24 when x is 4. The same process applies whenever you simplify expressions. Always perform the arithmetic operations carefully.

By simplifying correctly, you ensure the accurate evaluation of the algebraic expression.

Evaluating algebraic expressions involves finding the value of the expression for given variable values. Let's evaluate the expression \[2x + x^2 \] for x = 6. Start by substituting 6 for x: \[2(6) + 6^2 \] Next, perform the calculations: \[2(6) = 12 \] and \[6^2 = 36 \] Then, add these results to find the expression's value: \[12 + 36 = 48 \] Therefore, when x = 6, the value of the expression is 48.

This example shows how substituting and calculating leads you to evaluating the algebraic expression's value accurately.

Substitution of variables means replacing a variable with a specific value. It's a key step in evaluating expressions. Consider our expression \[2x + x^2 \] To find its value when x is 4, substitute 4 into the expression: \[2(4) + 4^2 \] Next, solve the substituted expression step-by-step. For the first part: \[2(4) = 8 \] And for the second part: \[4^2 = 16 \] Finally, add these results: \[8 + 16 = 24 \] Now repeat for x = 6: \[2(6) + 6^2 \] Calculate the first part: \[2(6) = 12 \] And the second part: \[6^2 = 36 \] Add the results: \[12 + 36 = 48 \] This shows how substituting the variable with specific values helps in solving the equation.