Chapter 8.4, Problem 3GP

a.

To determine

To determine the new area of the garden in square of a binomial.

Answer to Problem 3GP

  $g^2+6g+9$

Explanation of Solution

Given:

Size of the garden $g$ feet long and $g$ feet wide. Adding $3$ feet to the long and width.

Formula used:

Area of square $={(side)}^2$

  ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

As from the given information, the garden is square in shape,

Previous length $=g$ feet; width $=g$ feet,

After adding $3$ feet,

New length $=g+3$ feet; width $=g+3$ feet,

  $\Rightarrow$ New Area $={(side)}^2$

  $\Rightarrow$ New Area $={(g+3)}^2$

  $\Rightarrow$ New Area $=g^2+6g+9$ square feet

[ $\because {(a+b)}^2=a^2+2ab+b^2$ ]

Conclusion:

Therefore, the new area of the garden in square of a binomial is $g^2+6g+9$ square feet.

b.

To determine

To solve the square of a binomial.

Answer to Problem 3GP

  $g^2+6g+9$

Explanation of Solution

Given:

The area of the garden is ${(g+3)}^2$

Formula used:

  ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

As from the previous part, the area is ${(g+3)}^2.$

  $\Rightarrow$ New Area $={(g+3)}^2$

  $\Rightarrow$ New Area $=g^2+6g+9$ square feet

[ $\because {(a+b)}^2=a^2+2ab+b^2$ ]

Conclusion:

Therefore, the solved square of a binomial expression is $g^2+6g+9$ square feet.