### Home > A2C > Chapter 12 > Lesson 12.1.4 > Problem12-66

12-66.

Use algebra to demonstrate that each pair of expressions in parts (a) and (b) below are equivalent.

1. $\frac { k ( k + 1 ) } { 2 } + k + 1$and $\frac { ( k + 1 ) ( k + 2 ) } { 2 }$

Simplify and find a common denominator in the first expression:

$\frac{k^2+k+2k+2}{2}$

Now combine like terms and factor.

1. $\frac { k ( 7 k - 1 ) } { 2 } + 7 ( k + 1 ) - 4$and $\frac { ( k + 1 ) ( 7 k + 6 ) } { 2 }$

Use the same method as in part (a).