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4. Steps to calculate the value of algebraic expressions

Now we have to find out the values of algebraic expressions using the given variables.

Steps to find the value of the algebraic expression:

Step \(1\): Understand the problem first and then fix the variable and write the algebraic expression.

Step \(2\): Substitute each variable by the given numerical value to get an arithmetical expression.

Step \(3\): Try to solve or simplify the arithmetical expression by the BIDMAS method.

Step \(4\): Now, the final value you obtained is the required value of the expression.

Example:

Question I)

Consider the algebraic expression

13 m - 9 n - 8

and the value of \(m=\) 12 and \(n=\) 4.

Now substitute the values of \(m\) and \(n\), we get

\begin{array}{l} = 13 (12) - 9 (4) - 8 \\ = 156 - 36 - 8 \\ = 156 - 44 \\ = 112 \end{array}

Therefore, the value of the algebraic expression

13 m - 9 n - 8

\(=\) 112.

Question II)

Consider the algebraic expression

m^{2} - 4 n^{2} + 4

with the value of \(m=\) 12 and \(n=\) 4.

Now substitute the values of \(m\) and \(n\), we get

\begin{array}{l} = 12^{2} - 4 (4^{2}) + 4 \\ = 144 - 4 (16) + 4 \\ = 144 - 64 + 4 \\ = 148 - 64 \\ = 84 \end{array}

Therefore, the value of the algebraic expression

m^{2} - 4 n^{2} + 4

\(=\) 84.

Question III)

Consider the algebraic expression is

2 m^{2} - {8 n}^{2} + 13

with the value of \(m=\) 12 and \(n=\) 4.

Now substitute the values of \(m\) and \(n\), we get

\begin{array}{l} = 2 (12^{2}) - 8 (4^{2}) + 13 \\ = 2 (144) - 8 (16) + 13 \\ = 288 - 128 + 13 \\ = 301 - 128 \\ = 147 \end{array}

Therefore, the value of the algebraic expression

2 m^{2} - {8 n}^{2} + 13

\(=\) 147.

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