What is the middle term of the product of (x + 5)(x + 2)?

Solution:

Multiplying the expressions within the two brackets we have:

(x + 5)(x + 2) = (x + 5)x + (x + 5)2 [Using distributive property]

=  x² + 5x + 2x + 10

=  x² + 7x + 10

The middle term of the final expression is 7x

Consider another example: what is the middle term of the product (2x + 7)(3x + 8)?

(2x + 7)(3x + 8) = (2x + 7)(3x) + (2x + 7)8 

=  6x² + 21x + 16x + 56

=  6x² + 37x + 56

The middle term of the above final expression is 37x

What is the middle term of the product of (x + 5)(x + 2)?

Summary:

The middle term of the product of (x + 5)(x + 2) is 7x.