Evaluate an algebraic expression by substitution

Assigned value

\(\displaystyle x=-4\)

Find the value of the expression

Move the input to negative and positive positions. Compare the square with the negative of the square

At negative inputs, how do the two result columns compare?

Substitute before calculating

Use the same assigned value every time its pronumeral appears. Bracket a negative value so its sign stays attached. Follow the operation order within each group

1. 1Replace every occurrence Keep the negative sign with each substituted value \(\displaystyle 2(-4)^2+3(-4)-4\)
2. 2Evaluate the power The exponent applies to the base before the coefficient multiplies it \(\displaystyle 2\times16+3(-4)-4\)
3. 3Multiply the first term Multiply the squared value by its coefficient. Keep the remaining terms \(\displaystyle 32+3(-4)-4\)
4. 4Multiply the second term A positive coefficient times the negative assigned value gives a negative product \(\displaystyle 32-12-4\)
5. 5Subtract left to right Carry the final term through the first subtraction \(\displaystyle 20-4\)
6. 6Finish the subtraction Remove the final constant to obtain the value \(\displaystyle 16\)

Assigned values

\(\displaystyle x=-3,\quad y=5\)

Evaluate the expression

Evaluate the power and the grouped sum before multiplying and subtracting

Assigned values

\(\displaystyle p=-\frac34,\quad q=\frac12\)

Find the exact value

Square the numerator and denominator of the bracketed fraction. Keep the result exact when adding

Starting values

\(\displaystyle \begin{gathered}x=-3\\2x^2+5\end{gathered}\)

Where is the first error in the student's working?

Complete groups before combining them

For a quotient, work out the whole numerator and denominator. For a product of groups, work out each factor. Keep fractions exact until the calculation is finished

1. 1Substitute Keep the numerator and denominator intact \(\displaystyle \frac{(-4)^2+2}{4+2}\)
2. 2Evaluate the power Square the bracketed base in the numerator \(\displaystyle \frac{16+2}{4+2}\)
3. 3Complete the numerator Add the terms above the fraction bar, keeping the denominator \(\displaystyle \frac{18}{4+2}\)
4. 4Complete the denominator Add the terms below the fraction bar, keeping the numerator \(\displaystyle \frac{18}{6}\)
5. 5Divide The denominator is nonzero, so the quotient is defined \(\displaystyle 3\)

Assigned values

\(\displaystyle \begin{gathered}x=-\frac32,\quad y=\frac34\\z=-2\end{gathered}\)

Evaluate the product exactly

Evaluate each complete group, then multiply the two results

Assigned values

\(\displaystyle \begin{gathered}x=-2,\quad y=-3\\z=4\end{gathered}\)

Find the exact value

Calculate the whole quotient and the whole product before adding them. Keep the quotient exact