MATHS""20FUN

1) (2a-b)^(4a^2+2ab+b^2)^2
Don't know...so difficult

2) (a+b)(a-b)(a^2-ab+b^2)(a^2+ab+b^2)
=(a^2-ab+ab-b^2)(a^4+a^3 b+a^2 b^2-a^3 b-a^2 b^2-ab^3+a^2 b^2+ab^3+b^4)
=(a^2-b^2)(a^4+a^2b^2+b^4)
=(a^6+a^4b^2+a^2b^4-a^4b^2-a^2b^4-b^6)
=a^6-b^6

1) (2a - b)^(4a² + 2ab + b²)²
= (2a - b)^(16·a^4 + 8a³b + 4a²b² + 8a³b + 4a²b² + 2ab³ + 4a²b² + 2ab³ + b^4)
= 10^log[(2a - b)^(16·a^4 + 8a³b + 4a²b² + 8a³b + 4a²b² + 2ab³ + 4a²b² + 2ab³ + b^4)]
= 10^log[(2a - b)^(16·a^4 + 16a³b + 12a²b² + 4ab³ + b^4)]
= 10^[(16·a^4 + 16a³b + 12a²b² + 4ab³ + b^4)·log(2a - b)]
= 10^[16·a^4·log(2a - b) + 16a³b·log(2a - b) + 12a²b²·log(2a - b) + 4ab³·log(2a - b) + b^4·log(2a - b)]
= 10^[log(2a - b)^(16·a^4) + log(2a - b)^(16a³b) + log(2a - b)^(12a²b²) + log(2a - b)^(4ab³) + log(2a - b)^(b^4)]
= 10^log(2a - b)^(16·a^4) + 10^log(2a - b)^(16a³b) + 10^log(2a - b)^(12a²b²) + 10^log(2a - b)^(4ab³) + 10^log(2a - b)^(b^4)
= (2a - b)^(16·a^4) + (2a - b)^(16a³b) + (2a - b)^(12a²b²) + (2a - b)^(4ab³) + (2a - b)^(b^4) //

是否寫錯題目?本為 (2a - b) x (4a² + 2ab + b²)² ?
若是, [(2a) - b]·[(2a)² + (2a)·b + b²]²
= [(2a) - b]·[(2a)² - 2(2a)·b + b² + 3(2a)·b]²
= [(2a) - b]·[ [(2a) - b]² + 3(2a)·b]²
= [(2a) - b]²·[ [(2a) - b]² + 3(2a)·b]² / (2a - b)
= [ ((2a) - b)·((2a) - b)² + ((2a) - b)·3(2a)·b ]² / (2a - b)
= [ ((2a) - b)³ + 3(2a)·b·((2a) - b) ]² / (2a - b)
= [ ((2a) - b)³ + 3(2a)²b - 3(2a)b² ]² / (2a - b)
= [ (2a)³ - 3(2a)²·b + 3(2a)·b² - b³ + 3(2a)²b - 3(2a)b² ]² / (2a - b)
= [ (2a)³ - b³ ]² / (2a - b)
= ( 8a³ - b³ )² / (2a - b) //

2) (a + b)·(a - b)·(a² - ab + b²)·(a² + ab + b²)
= (a² + ba - ab - b²)·(a^4 - a³b + a²b² + a³b - a²b² + ab³ + a²b² - ab³ + b^4)
= (a² - b²)·(a^4 +a²b² + b^4)
= [(a²) - (b²)]·[ (a²)² + (a²)·(b²) + (b²)² ]
= [(a²) - (b²)]·[ (a²)² - 2(a²)·(b²) + (b²)² + 3(a²)·(b²) ]
= [(a²) - (b²)]·[ [(a²) - (b²)]² + 3(a²)·(b²) ]
= [(a²) - (b²)]³ + 3(a²)·(b²)·[(a²) - (b²) ]
= [(a²) - (b²)]³ + 3(a²)²·(b²) - 3(a²)·(b²)²
= [(a²)³ - 3(a²)²·(b²) + 3(a²)·(b²)² - (b²)³] + 3(a²)²·(b²) - 3(a²)·(b²)²
= (a²)³ - (b²)³
= a^6 - b^6 //