Question

A. Write an expression for the area of the shaded region.

Answer 1

Answer:

A. $25x² - 64$

B. $(5x + 8)(5x - 8)$

Step-by-step explanation:

A. The area of the shaded region = area of the whole large square - area of the 4 smaller squares

= (5x*5x) - 4(4*4)

Area of shaded region = $25x^2 - 64$

B. The expression, $25x^2 - 64$, is the difference of two perfect squares, 25x² and 64. Therefore, apply the rule of factoring difference of two perfect squares.

Thus, $a^2 - b^2 = (a + b)(a - b)$

Therefore, the expression of the are of the shaded region can be expressed in factored form as:

$25x^2 - 64 = (5x + 8)(5x - 8)$