因式分解（x+y)^4-7(x+y)²-1442x²(x-15)-16x6(a+b)²+2b(a+b)-20b²3(p-q)²-7(p²-q²)-6(p+q)²(x-1)(x+2)(x-3)(x+4)+24方程2x²-4x+y²+12y+38=0

Question

因式分解
（x+y)^4-7(x+y)²-144
2x²(x-15)-16x
6(a+b)²+2b(a+b)-20b²
3(p-q)²-7(p²-q²)-6(p+q)²
(x-1)(x+2)(x-3)(x+4)+24
方程
2x²-4x+y²+12y+38=0

Answer 1

（x+y)^4-7(x+y)²-144=[(x+y)²-16][(x+y)²+9]=(x+y+4)(x+y-4)(x²+2xy+y²+9
2x²(x-15)-16x=2x[x(x-15)-8]=2x(x²-15x-8)
6(a+b)²+2b(a+b)-20b²=2*[(a+b)²+b(a+b)-10b²]=2[(a+b+2b)(3a+3b-5b)]=2(a+3b)(3a-2b)
3(p-q)²-7(p²-q²)-6(p+q)²=[(p-q)-3(p+q)][3(p-q)+2(p+q)]=(-2p-4q)*(5p-q)=-2(2+2q)(5p-q)
(x-1)(x+2)(x-3)(x+4)+24
方程
2x²-4x+y²+12y+38=0
2x²-4x+2+y²+12y+36=0
2(x-1)²+(y+6)²=0
x-1=0,y+6=0
x=1,y=-6