Chapter 8.7, Problem 1P

a.

To determine

To write: The factored form of the given expression.

Explanation of Solution

Given information:

The given expression is $x^2+6x+9$

Calculation:

Factorize $x^2+6x+9$

  $\begin{array}{l}{x}^2+6x+9\\ =x^2+3x+3x+9\\ =x(x+3)+3(x+3)\\ =(x+3)(x+3)\end{array}$

Hence, the factored form of given expression is $(x+3)(x+3)$

b.

To determine

To write: The factored form of the given expression.

Explanation of Solution

Given information:

The given expression is $x^2-14x+49$

Calculation:

Factorize $x^2-14x+49$

  $\begin{array}{l}{x}^2-14x+49\\ =x^2-7x-7x+49\\ =x(x-7)-7(x-7)\\ =(x-7)(x-7)\end{array}$

Hence, the factored form of given expression is $(x-7)(x-7)$