Answer:
A. [tex] 25x² - 64 [/tex]
B. [tex] (5x + 8)(5x - 8) [/tex]
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 = [tex] 25x^2 - 64 [/tex]
B. The expression, [tex] 25x^2 - 64 [/tex], is the difference of two perfect squares, 25x² and 64. Therefore, apply the rule of factoring difference of two perfect squares.
Thus, [tex] a^2 - b^2 = (a + b)(a - b) [/tex]
Therefore, the expression of the are of the shaded region can be expressed in factored form as:
[tex] 25x^2 - 64 = (5x + 8)(5x - 8) [/tex]
