math.f.2

1. 設四分一圓半徑為r
四分一圓邊長 = 弧長 + 2半徑
= 2πr / 4 + 2r
= (π / 2 + 2)r = 32 cm
r = 32 / (π / 2 + 2)
r = 8.96 cm
四分一圓面積 = πr2 / 4 = π(8.96)2 / 4 = 63.1 cm2

2. (x + y)3 – 8(x – y)3 ;Use identity a3 – b3 = (a – b)(a2 + ab + b2)
= (x + y)3 – (2x – 2y)3
= (x + y – 2x + 2y)[(x + y)2 + (x + y)(2x – 2y) + (2x – 2y)2]
= (3y – x)(x2 + 2xy + y2 + 2x2 – 2y2 + 4x2 – 8xy + 4y2)
= (3y – x)(7x2 – 6xy + 3y2)