中二Factorization~15points!

1) (x+y)²-a(x+y)=(x+y)(x+y-a)
2) (x+3y)²-(x+3y)(x+2y)=(x+3y)[(x+3y)-(x+2y)]=y(x+3y) 3) x²-16=x²-4²=(x+4)(x-4) 4) -2x²y²+32=2(16-x²y²)=2[4²-(xy)²]=2(4+xy)(4-xy) 5) 9-6(p+q)+(p+q)²=(p+q)²-2(p+q)(3)+3²=(p+q+3)² 6) x³-4x²+4x=x(x²-4x+4)=x[x²-2(x)(2)+2²]=x(x-2)²
p.s.Important rules:1) ab+ac=a(b+c)2) a²-b²=(a+b)(a-b)3) a²+2ab+b²=(a+b)²4) a²-2ab+b²=(a-b)²

1) (x+y)²-a(x+y) 抽出(x+y) =(x+y)(x+y-a)
2) (x+3y)²-(x+3y)(x+2y) 抽出(x+3y) =(x+3y)[(x+3y)-(x+2y)] =y(x+3y)
3) x²-16 =x²-4² (使用平方差) =(x+4)(x-4)
4) -2x²y²+32 =2(16-x²y²) (抽出共同的2) =2[4²-(xy)²] (再使里面的数变成平方差) =2(4+xy)(4-xy)
5) 9-6(p+q)+(p+q)² =3²-3x2(p+q)+(p+q)² (使用完全平方)
={3-(p+q)}²
=(3-p-q)²


6) x³-4²+4x =x(x²-4x+4) (抽出共同的X) =x[x²-2(x)(2)+2²] (再使里面的数变成完全平方) =x(x-2)²