Chapter 8.4, Problem 63PFA

a.

To determine

To determine the expression of area of the square of side $2x+4$ units.

Answer to Problem 63PFA

  $4x^2+16x+16$ square units

Explanation of Solution

Given:

Sides of the square $=2x+4$

Formula used:

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

  ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

Given, sides of the square $=2x+4$

Area of square $={(2x+4)}^2$

  $={(2x)}^2+2\times 2x\times 4+4^2$  [ $\because$ ${(a+b)}^2=a^2+2ab+b^2$ ]

  $=4x^2+16x+16$ square units

Conclusion:

Therefore, area of square is $4x^2+16x+16$ square units.

b.

To determine

To determine the expression of area of the rectangle of length $5x+3$ units and width $5x-3$ .

Answer to Problem 63PFA

  $25x^2-9$ square units

Explanation of Solution

Given:

Rectangle of length $5x+3$ units and width $5x-3$

Formula used:

Area of rectangle $=\text{length×width}$

  $(a+b)(a-b)=a^2-b^2$

Calculation:

Given, the rectangle of length $5x+3$ units and $\text{width}$

  $5x-3$ .

Area of rectangle $=\text{length×width}$

  $=(5x+3)(5x-3)$

  $={(5x)}^2-3^2$  [ $\because$ $(a+b)(a-b)=a^2-b^2$ ]

  $=25x^2-9$ square units

Conclusion:

Therefore, area of rectangle is $25x^2-9$ square units.

c.

To determine

To determine the difference in the expression of the area between the square and the rectangle.

Answer to Problem 63PFA

  $21x^2-16x-25$ square units

Explanation of Solution

Given:

Area of square $=4x^2+16x+16$ square units

Area of rectangle $=25x^2-9$ square units

Calculation:

From the above two subparts,

Area of square $=4x^2+16x+16$ square units

Area of rectangle $=25x^2-9$ square units

Difference in the area between the square and the rectangle $=$ Area of rectangle $-$ Area of square

  $=(25x^2-9)-(4x^2+16x+16)$

  $=21x^2-16x-25$ square units

Conclusion:

Therefore, difference in the area between the square and the rectangle is $21x^2-16x-25$ square units.