Evaluate (a + b)² for a = 2 and b = 3.

Solution:

(a + b)² = a² + b² + 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

= 5²

= 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

= 7² - 3²

= 49 - 9

= 40

Alternatively

(a + b)² - (a - b)²

= a² + b² + 2ab - (a² + b² - 2ab)

= a² + b² + 2ab - a² - b² + 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.