# Evaluate (a + b)^{2} for a = 2 and b = 3.

**Solution:**

(a + b)^{2} = a^{2} + b^{2} + 2ab

= (2)^{2} + (3)^{2} + 2(2)(3)

= 4 + 9 + 12

= 25

The values of a and b could have been directly substituted in the algebraic expression (a + b)^{2} as shown below:

(a + b)^{2} = (2 + 3)^{2}

= 5^{2}

= 25

Which is the same result found earlier.

Another example could be: Evaluate (a + b)^{2} - (a - b)^{2} when a = 5 and b = 2

Substituting the values of a and b in the expression gives:

(5 + 2)^{2} - (5 - 2)^{2}

= 7^{2} - 3^{2}

= 49 - 9

= 40

Alternatively

(a + b)^{2} - (a - b)^{2}

= a^{2} + b^{2} + 2ab - (a^{2} + b^{2} - 2ab)

= a^{2} + b^{2} + 2ab - a^{2} - b^{2} + 2ab)

= 4ab

=4(5)(2)

= 40

## Evaluate (a + b)^{2} for a = 2 and b = 3.

**Summary:**

On evaluating (a + b)^{2} for a = 2 and b = 3, we get the result as 25.

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