因式分解(計算題~form2)

1a 因為a^2 - b^2 = (a+b)(a-b)

所以 (開方300+開方3)(開方300-開方3)
= (開方300)^2 - (開方3)^2
= 300 -3
= 297

2a 因為a^3 - b^3 = (a-b) (a^2 - ab + b^2)

所以 27- x^3
= 3^3 - x^3
= (3-x) (9 - 3x + x^2)

2b 289 - x^6y^4
= 17^2 - (x^3y^2)^2
= (17 + x^3y^2) (17 - x^3y^2)

2c a^2/64 - 9b^2/4
= (a/8)^2 - (3b/2)^2
= (a/8 + 3b/2) (a/8 - 3b/2)
如果要通埋分母
= [(a+12b)/8)] [(a-12b)/8)]

1. (a). (√300 + √3) (√300 - √3)
= (√300)^2 - (√3)^2
= 300 - 3
= 297

2. (a).27 - x^3
= 3^3 - x^3
= (3 - x) (3^2 + 3x + x^2)
= (3 - x) (9 + 3x + x^2)

(b). 289 - x^6y^4
= 17^2 - (x^3y^2)^2
= (17 + x^3y^2) (17 - x^3y^2)

(c). a^2/64 - 9b^2/4
= a^1/32 - 9b ^2
= (a^1/64)^2 - (3b)^2
= (a^1/64 - 3b) (a^1/64 + 3b)